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PDE/Applied Math Seminar

Institute Seminar

Theoretical Physics Seminar

Fall 14 course: S311

 Publications

## 2010-Present

[109] Tian Ma & Shouhong Wang, Weaton model of elementary particles and decay mechanism, IU Institute for Scientific Computing and Applied Mathematics Preprint Series, #1304; see also arXiv:1212.4893

[108] T. Sengul, J. Shen and S. Wang, Pattern Formations of 2D Rayleigh-Benard Convection with No-Slip Boundary Conditions for the Velocity at the Critical Length Scales

[107] Tian Ma & Shouhong Wang, Structure and Stability of Matter, IU Institute for Scientific Computing and Applied Mathematics Preprint Series, #1303; see also arXiv:1212.4893

[106] Tian Ma & Shouhong Wang, Duality of Weak Interaction, IU Institute for Scientific Computing and Applied Mathematics Preprint Series, #1302; see also arXiv:1212.4893

[105] Tian Ma & Shouhong Wang, Duality of Strong Interaction, IU Institute for Scientific Computing and Applied Mathematics Preprint Series, #1301; see also arXiv:1212.4893

[104] Tian Ma & Shouhong Wang, Unified Field Equations Coupling Four Forces and Principle of Interaction Dynamics, October 2012, arXiv:1210.0448

[103] Tian Ma & Shouhong Wang,Dynamic Transition and Pattern Formation for Chemotactic Systems

[102] Chun-Hsiung Hsia, Chang-Shou Lin, and T. Ma and S. Wang, Tropical Atmospheric Circulations with Humidity Effects

[101] Taylan Sengul and Shouhong Wang, Pattern Formation and Dynamic Transition for Magnetohydrodynamic Convection

[100] Honghu Liu, Taylan Sengul, Shouhong Wang and Pingwen Zhang, Dynamic Transitions and Pattern Formations for Cahn-Hilliard Model with Long-Range Repulsive Interactions

[99] Tian Ma and Shouhong Wang, Unified Field Theory and Principle of Representation Invariance, Applied Mathematics and Optimization, to appear; see also December, 2012, arXiv:1212.4893

[98] Tian Ma & Shouhong Wang, Gravitational Field Equations and Theory of Dark Matter and Dark Energy, Discrete and Continuous Dynamical Systems, Ser. A, 34:2(2014); see also arXiv:1206.5078

[97] Shouhong Wang and Ping Yang, Remarks on the Rayleigh-Benard Convection on Spherical Shells, J. Math Fluid Mech., 15:3(2013), pp 537-552

[96] Henk Dijkstra, Taylan Sengul and Shouhong Wang, Dynamic Transitions of Surface Tension Driven Convection, Physica D, Volume 247, Issue 1, 15 March 2013, Pages 7-17

[95] Taylan Sengul and Shouhong Wang, Pattern Formation in Rayleigh--Benard Convection, Communication of Mathematical Sciences, 11:1 (2013), 315-343

[94] Honghu Liu, Taylan Sengul and Shouhong Wang, Dynamic Transitions for Quasilinear Systems and Cahn-Hilliard equation with Onsager mobility, Journal of Mathematical Physics, 53, 023518 (2012); doi: 10.1063/1.3687414

[93] Tian Ma and Shouhong Wang, Third-Order Gas-Liquid Phase Transition and the Nature of Andrews Critical Point, AIP Advances, 1, 042101 (2011); doi: 10.1063/1.3650703

[92] Tian Ma and Shouhong Wang, Phase Transitions for Belousov-Zhabotinsky Reactions, Mathematical Methods in Applied Sciences, 34:11(2011), 1381-1397

[91] Tian Ma and Shouhong Wang, El Nino Southern Oscillation as Sporadic Oscillations between Metastable States, Advances in Atmospheric Sciences, 28:3 (2011), 612-622

[90] J. Bona, C. Hsia, T. Ma and S. Wang, Hopf bifurcation for two-dimensional doubly-diffusive convection, Applicable Analysis, dedicated to Solonnikov on the occasion of his 75th birthday, 1563-504X, Volume 90, Issue 1, First published 2011, Pages 5-30

[89] Tian Ma and Shouhong Wang, Phase Transitions for the Brusselator Model, Journal of Mathematical Physics, 52:033501 (2011), 1-23

[88] Tian Ma and Shouhong Wang, Dynamic Transition Theory for Thermohaline Circulation, Physica D, 239:3-4, 167-189

[87] C. Hsia, Tian Ma and Shouhong Wang, Rotating Boussinesq Equations: Dynamic Stability and Transitions, Discrete Contin. Dyn. Syst., 28:1(2010), 99--130

[86] Tian Ma and Shouhong Wang, Tropical Atmospheric Circulations: Dynamic Stability and Transitions, DCDS-A, 26:4(2010), 1399-1417

[85] Tian Ma and Shouhong Wang, Dynamic Bifurcation and Stability of the Taylor Problem, Dedicated to Roger Temam on the occasion of his 70th birthday, Chinese Annuals of Math. Ser. B, Volume 31, Number 6, 953-974, DOI: 10.1007/s11401-010-0610-7

## 2005-2009

[84] Tian Ma and Shouhong Wang, Phase Separation of Binary Systems, Physica A: Statistical Mechanics and its Applications, 388:23 (2009), 4811-4817

[83] Tian Ma and Shouhong Wang, Boundary Layer and Interior Separations in the Taylor--Couette--Poiseuille Flow, Journal of Mathematical Physics, 50:3(2009), 1-29

[82] Tian Ma and Shouhong Wang, Phase Transition and Separation for Mixture of Liquid He-3 and He-4, in Lev Davidovich Landau and his Impact on Contemporary Theoretical Physics, Horizons in World Physics, Volume 264, Edited by A. Sakaji and I. Licata, pp. 107-119

[81] Tian Ma and Shouhong Wang, Cahn-Hilliard Equations and Phase Transition Dynamics for Binary Systems, DCDS-B, 11:3(2009), 741-784

[80] Hans Kaper, Shouhong Wang and Masoud Yari, Dynamic Transitions of Turing Patterns, Nonlinearity, 22(2009), 601-626

[79] Tian Ma and Shouhong Wang, Dynamic Transitions for PVT Systems, in a special issue dedicated to Ciprian Foias on the occasion of his 70th birthday, Indiana University Mathematics Journal, 57 (2008), 2861-2890

[78] Tian Ma and Shouhong Wang, Superfluidity of helium-3, Physica A: Statistical Mechanics and its Applications, 387:24 (2008), 6013-6031

[77] Tian Ma and Shouhong Wang, Dynamic Model and Phase Transitions for Liquid Helium, Journal of Mathematical Physics, 49:073304 (2008), 1-18

[76] Tian Ma and Shouhong Wang, Dynamic Transitions for Ferromagnetism, {\it Journal of Mathematical Physics}, 49:053506 (2008), 1-18

[75] Tian Ma and Shouhong Wang, Principle of Exchange of Stabilities and Dynamic Transitions, in a special issue dedicated to the memory of Prof. J. L. Lions on the occasion of his 80th birthday, Georgian Mathematical Journal, 15:3 (2008), 581--590 (with Tian Ma)

[74] C. Hsia and T. Ma and S. Wang, Attractor bifurcation of three dimensional double-diffusive
convection, ZAA, 27(2008), 233-252

[73] Jianping Li and Shouhong Wang, Some Mathematical and Numerical Issues in Geophysical Fluid Dynamics and Climate Dynamics, Communications in Computational Physics, 3:4(2008), 759-793

[72] C. Hsia, T. Ma and S. Wang, Bifurcation and stability of two-dimensional double-diffusive
convection, CPAA, 7:1(2008), 23-48

[71] Tian Ma and Shouhong Wang, Dynamic Transitions in classical and geophysical fluid dynamics, Proc. Appl. Math. Mech., 7 (2007), 1101503-1101504

[70] R. Samelson, R. Temam, C. Wang and S. Wang, A fourth order numerical method for the planetary geostrophic equations with inviscid geostrophic balance, Numerische Mathematik, 107(2007), 669-705

[69] Tian Ma and Shouhong Wang, Rayleigh-Benard Convection: Dynamics and Structure in the Physical Space, Comm. Math. Sci., 5:3(2007), 553-574

[68] Chun-Hsiung Hsia and Tian Ma and Shouhong Wang, Stratified Rotating Boussinesq Equations in Geophysical Fluid Dynamics : Dynamic Bifurcation and Periodic Solutions, J. Math. Phys., 48:065602 (2007), 1-20

[67] Tian Ma and Shouhong Wang. Stability and bifurcation of the Taylor problem, Archive Rational Mechanics and Analysis, 181:1(2006), 149-176

[66] Tian Ma and Shouhong Wang, Block structure and block stability of incompressible flows,
DCDS-B, 6:1(2006), 169 - 184

[65] Tian Ma and Shouhong Wang, Bifurcation and Stability of Superconductivity, Dedicated
to Professor Louis Nirenberg on the occasion of his eightieth birthday, Journal of Mathematical Physics, 46(2005)

[64] M. Ghil and T. Ma and S. Wang, Structural Bifurcation of 2-D Incompressible Flows
with Dirichlet Boundary Conditions: Applications to Boundary-Layer Separation, SIAM J. Applied Math., 65:5(2005), 1576-1596

[63] Tian Ma and Shouhong Wang, Dynamic bifurcation of nonlinear evolution equations,
Chinese Annals of Mathematics, 26:2(2005), 185-206

[62] Tian Ma and Shouhong Wang, Periodic structure of 2-D Navier-Stokes equations,
Journal of Nonlinear Science, 15:3(2005), 133-158

## 2000-2004

[61] T. Ma and S. Wang, Bifurcation of Nonlinear Equations: II. Dynamic Bifurcation
Methods and Applications of Analysis, 11:2(2004), 179-210

[60] T. Ma and S. Wang, Bifurcation of Nonlinear Equations: I. Steady State Bifurcation, Methods and Applications of Analysis, 11:2(2004), 155-178

[59] T. Ma and Jungho Park and S. Wang, Dynamic Bifurcation of the Ginzburg-Landau Equation, SIAM J. Applied Dynamics, 3:4(2004), 620-635

[58] M. Ghil, J. Liu, and C. Wang and S. Wang, Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow, Physica D, 197:1-2(2004), 149-173

[57] T. Ma and S. Wang, Dynamic Bifurcation and Stability in the Rayleigh-B\'enard Convection, Communication in Math. Sci., 2:2(2004), 159-183

[56] T. Ma and S. Wang, Interior Structural Bifurcation and Separation of $2-D$ Incompressible Flows, J. Math. Phy., 45:5(2004), 1762-1776

[55] T. Ma and S. Wang., Asymptotic Structure for Solutions of the Navier--Stokes
Equations, {Discrete and Continuous Dynamical Systems, 11:1(2004), 189-204

[54] T. Ma and S. Wang, Boundary Layer Separation and Structural Bifurcation
for 2-D Incompressible Fluid Flows, Discrete and Continuous Dynamical Systems, 10:1-2(2004), 459--472

[53] Z. Chen, M. Ghil and E. Simonnet and S. Wang, Hopf Bifurcation in Quasi-Geostrophic Channel Flow, SIAM J. Applied Math., 64:1(2004), 343-368

[52] T. Ma and S. Wang, Attractor bifurcation theory and its applications to Rayleigh-B\'enard convection, Communications on Pure and Applied Analysis, 2:4(2003), 591--599

[51] T. Ma and S. Wang, Rigorous Characterization of Boundary Layer Separations, Proc. of the Second MIT Conference on Computational Fluid and Solid Mechanics, Cambridge, MA, 2003

[50] R. Samelson, R. Temam and C. Wang and S. Wang, Surface Pressure Poisson Equation Formulation of the Primitive Equations: Numerical Schemes, SIAM J. Num. Anal., 41:3(2003), 1163-1194

[49] M. Ghil, K. Ide, E. Simonnet, R. Temam and S. Wang, Low-Frequency Variability in Shallow Water Models of the Wind-Driven Ocean Circulation. Part II: Time-Dependent Solutions, Journal of Physical Oceanography, 33(2003), 729-752

[48] M. Ghil, K. Ide, E. Simonnet, R. Temam and S. Wang, Low-Frequency Variability in Shallow Water Models of the Wind-Driven Ocean Circulation. Part I: Steady State Solutions,
Journal of Physical Oceanography, 33(2003), 712-728

[47] T. Ma and S. Wang, Topology of 2-D incompressible flows
and applications to geophysical fluid dynamics, Revista de la Real Academia de Ciencias (RACSAM), 93:6(2002), 447-459

[46] Qingfeng Ma, Shouhong Wang and Chengkui Zhong, Necessary and Sufficient Conditions of Global Attractors for Semigroups and Applications, Indiana University Math. J., 51:6(2002), 1541-1559

[45] }T. Ma and S. Wang, Structural Classification and Stability of Incompressible
Vector Fields, {Physica D, 171(2002), 107-126

[44] M. Ghil and T. Ma and S. Wang, Structural Bifurcation of 2-D Incompressible Flows,
Indiana University Mathematics Journal, 50:1(2001), 159-180

[43] T. Ma and S. Wang, A Generalized Version of the Poincare-Hopf Index Formula and its Applications to 2--D Incompressible Flows, Nonlinear Analysis: Real World Applications,
2(2001), 467-482

[42] T. Ma and S. Wang, Global structure of 2-D Incompressible Flows, Discrete and Continuous Dynamical Systems, 7:2(2001), 431-445

[41] T. Ma and S. Wang, Structure of 2D Incompressible Flows with the
Dirichlet Boundary Conditions, Discrete and Continuous Dynamical Systems, Ser. B, 1:1(2001),
29-41

[40] R. Samelson, R. Temam and S. Wang, Smooth solutions and attractor dimension bounds for planetary geostrophic ocean models, Quarterly Journal of Royal Meteorological Society, 126:566(2000), 1977-1981

[39] Z. Chen and S. Wang, Steady-state bifurcations of the three-dimensional Kolmogorov problem, Electron. J. Differential Equations, 2000(2000), 1-32 (with Z. Chen)

[38] T. Ma and S. Wang, Structural Evolution of the Taylor Vortices, Mathematical Modeling and Numerical Analysis, 34:2(2000), 419-437

[37] J.-L. Lions, R. Temam and S. Wang, On Mathematical Problems for the Primitive Equations of the Ocean: The Mesoscale Midlatitude Case, Nonlinear Analysis, 40(2000),
439-482

[36] T. Ma and S. Wang, Dynamics of 2--D Incompressible Flows, in Proceedings of The International Conference on Differential Equations and Computational Simulations, June 13-18, 1999, Chengdu, pp. 270-276

[35] R. Temam and S. Wang. Mathematical Problems in Meteorology and Oceanography,
Bull. Amer. Meteorol. Soc., 81:2(2000), 319-321

[34] R. Samelson, R. Temam and S. Wang, Remarks on the Planetary Geostrophic Model of
Gyre Scale Ocean Circulation, Differential and Integral Equations, 13(2000), 1--14

## 1995-1999

[33] J. Shen and T. Tachim Medjo and S. Wang, On a Wind-Driven, Double-Gyre, Quasi-Geostrophic Ocean Model: Numerical Simulations and Structural Analysis, Journal of Computational Physics, 155(1999), 387-409

[32] T. Ma and S. Wang, The Geometry of the Stream Lines of Steady States of the Navier--Stokes Equations, Nonlinear Partial Differentuial Equations, Edited by Gui-Qiang Chen and Emmanule DiBenedetto, Contemporary Mathematics, AMS, vol. 238 (1999), 193-202

[31] J. Shen and S. Wang, An Efficient Numerical Scheme for the Primitive Equations of
the Atmosphere, SIAM J. Numer. Analysis, 36:3(1999), 719-737

[30] T. Ma and S. Wang, Dynamics of Incompressible Vector Fields, Applied Math. Lett., 12(1999), 39-42

[29] S. Wang and M. Zhan, $L^p$ Solutions to the Time Dependent Ginzburg-Landau Equations of Superconductivity, Nonlinear Analysis, 36(1999), 661-677

[28] R. Samelson and R. Temam and S. Wang, Some Mathematical Properties of the Planetary Geostrophic Equations for Large-Scale Ocean Circulation, Applicable Analysis, 70:1-2(1999), 147-173

[27] M. Ghil, K. Ide, E. Simonnet, R. Temam and S. Wang, Successive bifurcations in a shallow-water ocean model, Dedicated to M. Holt on his 80th Birthday, in Sixteenth International Conference on Numerical Methods in Fluid Dynamics, Edited by Charles-Henri Bruneau, Lecture Notes in Physics, Vol 515, Springer-Verlag, pp. 225-230, 1998

[26] M. Cabral, B. Costa and R. Temam and S. Wang, The primitive equations of the atmosphere with chemistry, In Equations aux d\'eriv\'ees partielles et Applications, Articles d\'edi\'es \a J. L. Lions, 1998

[25] B. Wang and S. Wang, Gevrey Class Regularity for the Solutions of the
Ginzburg-Landau Equations of Superconductivity, Discrete and Continuous Dynamical Systems, 4:3(1998), 507-522

[24] H. Kaper, B. Wang and S. Wang, On the Determining Nodes for the Time Dependent
Ginzburg-Landau Equations of Superconductivity, Discrete and Continuous Dynamical Systems,
4:2(1998), 205-224

[23] J.-L. Lions, R. Temam and S. Wang, A Simple Model for the General Circulation of the Atmosphere, Dedicated Peter D. Lax and Louis Nirenberg on the Occasion of their 70th Birthdays, Comm. Pure Appl. Math., 50:8(1997), 707-752

[22] T. Tachim Medjo, R. Temam and S. Wang, Higher Order Approximation Equations for the Primitive Equations of the Atmosphere, Journal of Engineering Mathematics, Special issue on Large-Scale Numerical Modeling of Problems involving the Navier-Stokes equations, 32(1997), 237-256

[21] J.-L. Lions, O. Manley and R. Temam and S. Wang, Physical Interpretations of the Attractor for a Simple Model of Atmospheric Circulation, Journal of Atmosphere Sciences, 54:9(1997), 1137-1143

[20] J.-L. Lions, R. Temam and S. Wang, Splitting up Methods and Numerical Analysis of Some Multi-scale Problems, Computational Fluid Mechanics Journal, Special Issue Dedicated to A. Jameson, 5:2 (1996), 157-202

[19] Q. Tang and S. Wang, Time Dependent Ginzburg-Landau Equations of Superconductivity,
Physica D, 88(1995), 139-166

[18] O. Manley, R. Temam and S. Wang, Inertial Manifolds, Space Averaged Reynolds Equations, and the Separation of Scales in Turbulent Flows, Dedicated to W. Reynolds on the occasion of his 60th birthday, Physics of Fluids, 7:7(1995), 1791-1793

[17] J.-L. Lions, R. Temam and S. Wang, Mathematical Theory for the Coupled Atmosphere-Ocean Models, J. Math. Pures et Appl., 74:2 (1995), 105-163

[16] Q. Tang and S. Wang, Long Time Behavior of the Ginzburg-Landau Superconductivity Equations, Appli. Math. Lett, 8:2, 31-34 (1995)

## 1990-1994

[15] J.-L. Lions, R. Temam and S. Wang, Geostrophic Asymptotics of the Primitive Equations
of the Atmosphere, Topological Methods in Nonlinear Analysis, Special Issue Dedicated to Jean Leray, 4(1994), 253-287

[14] J.-L. Lions, R. Temam and S. Wang, Probl\emes \a Fronti\ere Libre pour les Mod\eles
Coupl\'es de l'Oc\'ean et de l'Atmosph\ere, C. R. Acad. Sci. Paris, S\'er. I,
318(1994), 1165-1171

[13] R. Temam and S. Wang, Inertial Forms of Navier-Stokes Equations
on the Sphere, J. Funct. Anal., 117:1(1993), 215-242

[12] J.-L. Lions, R. Temam and S. Wang, Numerical Analysis of Coupled Atmosphere-Ocean Models, Computational Mechanics Advance, 1(1993), 55-120, J.T. Oden ed., Elsevier

[11] J.-L. Lions, R. Temam and S. Wang, Models of the Coupled Atmosphere and Ocean,
Computational Mechanics Advance, Vol. 1, 1993, 3-54, J.T. Oden ed., Elsevier

[10] J.-L. Lions, R. Temam and S. Wang, Mod\eles et Analyse Math\'ematique du Syst\eme
Oc\'ean/Atmosph\ere, II. Couplage, C. R. Acad. Sci. Paris, S\'er. I, 316(1993), 211-215

[9] J.-L. Lions, R. Temam and S. Wang, Mod\eles et Analyse Math\'ematique du Syst\eme
Oc\'ean/Atmosph\ere, I. Structure des sous Syst\`emes, C. R. Acad. Sci. Paris, S\'er. I,
316(1993), 113-119

[8] J.-L. Lions, R. Temam and S. Wang, On the Equations of the Large-scale
Ocean, Nonlinearity, 5(1992), 1007-1053

[7] J.-L. Lions, R. Temam and S. Wang, New Formulations of the Primitive Equations of Atmosphere and Applications, Nonlinearity, 5(1992), 237-288

[6] S. Wang, Attractors for the 3D Baroclinic Quasi-Geostrophic Equations
of Large Scale Atmosphere, J. Math. Anal. Appl., 165(1992), 266-283

[5] S. Wang, On the 2D Model of Large Scale Atmospheric Motion: Well--Posedness
and Attractors, Nonlinear Analysis-TMA, 18:1(1992), 17-60

[4] S. Wang, Approximate Inertial Manifolds for the 2D Model of Atmosphere, Num. Funct. Anal. and Opt., 11:9-10(1990-91), 1043-1070

[3] S. Wang, On Stationary Solutions to the Equations of Large Scale Atmosphere, Nonlinear Analysis, W. Chen ed., Lanzhou University Press, 1989

[2] J. Chou and J. Huang and S. Wang, Some Properties of Solutions for the Equations of Large Scale Atmosphere: Nonlinear Adjustment to the Time Independent External Forcing, Science in China, 38(1989), 328-336

[1] S. Wang, Free Vibrations for a Class of Wave Equations with Strong
Resonance, Chinese Ann. Math., 10A:3(1989), 289-298

[0] S. Wang, On Solvability of the Equations of Large-Scale Atmospheric Equations, Ph D thesis, 1988.