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Global regularity to the two dimensional compressible Navier-Stokes equations with mass diffusion. (English) Zbl 1328.35146

Summary: For an isentropic compressible Navier-Stokes model with mass diffusion in a two dimensional bounded smooth domain, global existence and uniqueness of strong solution to the initial-boundary value problem is proved, without any size restriction on the initial data. The proof relies on global upper and lower positive bound for the density, which is a consequence of mass diffusion and obtained by De Giorgi-Nash-Moser’s estimate for solution to the second order parabolic equation.

MSC:

35Q30 Navier-Stokes equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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