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Global classical solutions to the 3D isentropic compressible Navier-Stokes equations in a bounded domain

Author:
Yu, Haibo  Zhao, Junning  


Journal:
NONLINEARITY


Issue Date:
2017


Abstract(summary):

In this paper, we study the global existence for classical solutions to the 3D isentropic compressible Navier-Stokes equations in a cuboid domain. Compared to the Cauchy problem studied in Hoff (1995 J. Differ. Equ. 120 215-54), Hoff (2005 J. Math. Fluid Mech. 7 315-38), Huang et al (2012 Commun. Pure Appl. Math. 65 549-85), some new thoughts are applied to obtain upper bounds for density. Precisely, through piecewise estimation and some time-depending a priori estimates, we establish time-uniform upper bounds for density under the assumption that the initial energy is small. The initial vacuum is allowed.


Page:
361---381


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