Overview
biography
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Chongsheng Cao, PhD, is a Professor in the Department of Mathematics and Statistics.
Ph.D. in Applied Mathematics, 1999. University of California, Irvine
research interests
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Nonlinear Partial Differential Equations
Nonlinear Dynamical Systems
Control Theory
Fluid Dynamics
Geophysics
Computational Mathematics
Scholarly & Creative Works
selected scholarly works & creative activities
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Article
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2021Global well-posedness of 2D chemotaxis Euler fluid systems. JOURNAL OF DIFFERENTIAL EQUATIONS. 294:251-264.Full Text via DOI: 10.1016/j.jde.2021.05.039 Web of Science: 000660507900008
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2020Global well-posedness for a rapidly rotating convection model of tall columnar structure in the limit of infinite Prandtl number. JOURNAL OF EVOLUTION EQUATIONS. 21:2923-2954.Full Text via DOI: 10.1007/s00028-020-00644-4 Web of Science: 000587959300001
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2020Global regularity for a rapidly rotating constrained convection model of tall columnar structure with weak dissipation. JOURNAL OF DIFFERENTIAL EQUATIONS. 269:8736-8769.Full Text via DOI: 10.1016/j.jde.2020.06.033 Web of Science: 000546572400032
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2020Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity. PHYSICA D. 412.Full Text via DOI: 10.1016/j.physd.2020.132606 Web of Science: 000564668400010
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2020On the Well-Posedness of Reduced 3D Primitive Geostrophic Adjustment Model with Weak Dissipation. JOURNAL OF MATHEMATICAL FLUID MECHANICS. 22.Full Text via DOI: 10.1007/s00021-020-00495-6 Web of Science: 000540799900003
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2018Global strong solutions for the three-dimensional Hasegawa-Mima model with partial dissipation. JOURNAL OF MATHEMATICAL PHYSICS. 59.Full Text via DOI: 10.1063/1.5022099 Web of Science: 000440588200004
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2017Strong solutions to the 3D primitive equations with only horizontal dissipation: Near H-1 initial data. JOURNAL OF FUNCTIONAL ANALYSIS. 272:4606-4641.Full Text via DOI: 10.1016/j.jfa.2017.01.018 Web of Science: 000399354600006
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2016Global Well-Posedness of the Three-Dimensional Primitive Equations with Only Horizontal Viscosity and Diffusion. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 69:1492-1531.Full Text via DOI: 10.1002/cpa.21576 Web of Science: 000379919000003
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2016Global regularity results for the 2D Boussinesq equations with partial dissipation. JOURNAL OF DIFFERENTIAL EQUATIONS. 260:1893-1917.Full Text via DOI: 10.1016/j.jde.2015.09.049 Web of Science: 000373536400034
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2015Finite-Time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 337:473-482.Full Text via DOI: 10.1007/s00220-015-2365-1 Web of Science: 000353505300001
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2014Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity. JOURNAL OF DIFFERENTIAL EQUATIONS. 257:4108-4132.Full Text via DOI: 10.1016/j.jde.2014.08.003 Web of Science: 000343187300007
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2014Local and Global Well-Posedness of Strong Solutions to the 3D Primitive Equations with Vertical Eddy Diffusivity. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. 214:35-76.Full Text via DOI: 10.1007/s00205-014-0752-y Web of Science: 000339718600002
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2014Small global solutions to the damped two-dimensional Boussinesq equations. JOURNAL OF DIFFERENTIAL EQUATIONS. 256:3594-3613.Full Text via DOI: 10.1016/j.jde.2014.02.012 Web of Science: 000334727000005
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2014THE 2D INCOMPRESSIBLE MAGNETOHYDRODYNAMICS EQUATIONS WITH ONLY MAGNETIC DIFFUSION. SIAM JOURNAL ON MATHEMATICAL ANALYSIS. 46:588-602.Full Text via DOI: 10.1137/130937718 Web of Science: 000333591800021
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2013Global Regularity for the Two-Dimensional Anisotropic Boussinesq Equations with Vertical Dissipation. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. 208:985-1004.Full Text via DOI: 10.1007/s00205-013-0610-3 Web of Science: 000318563300007
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2013Global Well-Posedness of an Inviscid Three-Dimensional Pseudo-Hasegawa-Mima Model. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 319:195-229.Full Text via DOI: 10.1007/s00220-012-1626-5 Web of Science: 000316490100005
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2013The 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion. JOURNAL OF DIFFERENTIAL EQUATIONS. 254:2661-2681.Full Text via DOI: 10.1016/j.jde.2013.01.002 Web of Science: 000315128100001
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2013Global regularity for an inviscid three-dimensional slow limiting ocean dynamics modelFull Text via DOI: 10.4310/CIS.2013.v13.n1.a4 Web of Science: 000213684600005
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2012Global solutions for the 2D NS-CH model for a two-phase flow of viscous, incompressible fluids with mixed partial viscosity and mobility. NONLINEARITY. 25:3211-3234.Full Text via DOI: 10.1088/0951-7715/25/11/3211 Web of Science: 000310525600011
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2012Global Well-Posedness of the 3D Primitive Equations with Partial Vertical Turbulence Mixing Heat Diffusion. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 310:537-568.Full Text via DOI: 10.1007/s00220-011-1409-4 Web of Science: 000301491400009
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2011Global Regularity Criterion for the 3D Navier-Stokes Equations Involving One Entry of the Velocity Gradient Tensor. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. 202:919-932.Full Text via DOI: 10.1007/s00205-011-0439-6 Web of Science: 000297348300005
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2011Global regularity results for the 2D Boussinesq equations with vertical dissipation. JOURNAL OF DIFFERENTIAL EQUATIONS. 251:1637-1655.Full Text via DOI: 10.1016/j.jde.2011.05.027 Web of Science: 000292897600013
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2011Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion. ADVANCES IN MATHEMATICS. 226:1803-1822.Full Text via DOI: 10.1016/j.aim.2010.08.017 Web of Science: 000284452900025
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2010The 2D Boussinesq equations with vertical viscosity and vertical diffusivity. JOURNAL OF DIFFERENTIAL EQUATIONS. 249:1078-1088.Full Text via DOI: 10.1016/j.jde.2010.03.021 Web of Science: 000279292300004
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2010Two regularity criteria for the 3D MHD equations. JOURNAL OF DIFFERENTIAL EQUATIONS. 248:2263-2274.Full Text via DOI: 10.1016/j.jde.2009.09.020 Web of Science: 000275785100003
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2010SUFFICIENT CONDITIONS FOR THE REGULARITY TO THE 3D NAVIER STOKES EQUATIONS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. 26:1141-1151.Full Text via DOI: 10.3934/dcds.2010.26.1141 Web of Science: 000272775400003
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2008Regularity Criteria for the Three-dimensional Navier-Stokes Equations. INDIANA UNIVERSITY MATHEMATICS JOURNAL. 57:2643-2661.Full Text via DOI: 10.1512/iumj.2008.57.3719 Web of Science: 000262386400007
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2008Regularity criterion for solutions of three-dimensional turbulent channel flows. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. 33:419-428.Full Text via DOI: 10.1080/03605300701454859 Web of Science: 000253729400005
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2007Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics. ANNALS OF MATHEMATICS. 166:245-267.Full Text via DOI: 10.4007/annals.2007.166.245 Web of Science: 000252508300007
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2005On the Clark-alpha model of turbulence: global regularity and long-time dynamics. JOURNAL OF TURBULENCE. 6:1-11.Full Text via DOI: 10.1080/14685240500183756 Web of Science: 000235709100001
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2004A 'horizontal' hyper-diffusion three-dimensional thermocline planetary geostrophic model: Well-posedness and long-time behaviour. NONLINEARITY. 17:1749-1776.Full Text via DOI: 10.1088/0951-7715/17/5/011
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2003Global Well-Posedness and Finite-Dimensional Global Attractor for a 3-D Planetary Geostrophic Viscous Model. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 56:198-233.Full Text via DOI: 10.1002/cpa.10056
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2001Numerical criterion for the stabilization of steady states of the Navier-Stokes equations. INDIANA UNIVERSITY MATHEMATICS JOURNAL. 50:37-95.Full Text via DOI: 10.1512/iumj.2001.50.2154
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2000Gevrey regularity for nonlinear analytic parabolic equations on the sphereFull Text via DOI: 10.1023/A:1009072526324
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1999The Navier-Stokes equations on the rotating 2 - D sphere: Gevrey regularity and asymptotic degrees of freedom. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. 50:341-360.Full Text via DOI: 10.1007/PL00001493
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Conference
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2002ASYMPTOTIC BEHAVIOR OF VISCOUS 1–D SCALAR CONSERVATION LAWS WITH NEUMANN BOUNDARY CONDITIONS. 306-324.Full Text via DOI: 10.1142/9789812778390_0025
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Preprint
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2013Small global solutions to the damped two-dimensional Boussinesq equationsFull Text via DOI: 10.48550/arxiv.1308.1723
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