Overview
overview
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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
Publications
selected scholarly works & creative activities
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Article
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2025Stability of 3D perturbations to 2D Navier-Stokes flows with vertical dissipation. Applied Mathematics Letters. 171.Full Text via DOI: 10.1016/j.aml.2025.109634 Web of Science: 001509127900001
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2025Stability of the 3D Navier-Stokes equations with anisotropic dissipation. Nonlinearity. 38.Full Text via DOI: 10.1088/1361-6544/adffda Web of Science: 001566978300001
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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 of the 3D primitive equations with horizontal viscosity and vertical diffusivity. Physica D : Non-linear phenomena. 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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2020Regularity “in Large” for the 3D Salmon’s Planetary Geostrophic Model of Ocean Dynamics. Mathematics of Climate and Weather Forecasting. 6:1-15.Full Text via DOI: 10.1515/mcwf-2020-0001
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2017Strong solutions to the 3D primitive equations with only horizontal dissipation: Near H1 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 model. Communications in Information and Systems. 13:97-122.Full 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. Series A. 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-α 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 Web of Science: 000224394800011
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2004Traveling Wave Solutions for a Class of One-Dimensional Nonlinear Shallow Water Wave Models. Journal of Dynamics and Differential Equations. 16:167-178.Full Text via DOI: 10.1023/b:jody.0000041284.26400.d0
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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 Web of Science: 000180052900002
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2000Gevrey regularity for nonlinear analytic parabolic equations on the sphere. Journal of Dynamics and Differential Equations. 12:411-433.Full 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 für Angewandte Mathematik und Physik. 50:341-360.Full Text via DOI: 10.1007/PL00001493 Web of Science: 000081003400001
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Numerical criterion for the stabilization of steady states of the Navier-Stokes equations. Indiana University Mathematics Journal. 50:37-96.Full Text via DOI: 10.1512/iumj.2001.50.2154 Web of Science: 000171494400003
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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
Research
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Contact
full name
- Chongsheng Cao
