GLOBAL SOLUTIONS TO A 3D AXISYMMETRIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY

doi:10.1007/s10473-022-0207-8

Abstract

Abstract: In this paper, we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosity μ is a positive constant and the bulk viscosity is λ(ρ) = ρ^β with β > 2, which is a situation that was first introduced by Vaigant and Kazhikhov in [1]. The global axisymmetric classical solution with arbitrarily large initial data in a periodic domain Ω = {(r, z)|r = √x² + y², (x, y, z) ∈ R³, r ∈ I ⊂ (0, +∞), −∞ < z < +∞} is obtained. Here the initial density keeps a non-vacuum state p > 0 when z → ±∞. Our results also show that the solution will not develop the vacuum state in any finite time, provided that the initial density is uniformly away from the vacuum.

Key words: Navier-Stokes equations, axisymmetric, density-dependent, classical solution

CLC Number:

35Q30

Mei WANG, Zilai LI, Zhenhua GUO. GLOBAL SOLUTIONS TO A 3D AXISYMMETRIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY[J].Acta mathematica scientia,Series B, 2022, 42(2): 521-539.

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References

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