INTERFACE BEHAVIOR AND DECAY RATES OF COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND A VACUUM*

doi:10.1007/s10473-024-0114-2

Abstract

Abstract: In this paper, we study the one-dimensional motion of viscous gas near a vacuum, with the gas connecting to a vacuum state with a jump in density. The interface behavior, the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficient $\mu(\rho)=\rho^{\alpha}$ for any $0<\alpha<1$; this includes the time-weighted boundedness from below and above. The smoothness of the solution is discussed. Moreover, we construct a class of self-similar classical solutions which exhibit some interesting properties, such as optimal estimates. The present paper extends the results in [Luo T, Xin Z P, Yang T. SIAM J Math Anal, 2000, 31(6): 1175-1191] to the jump boundary conditions case with density-dependent viscosity

Key words: decay rates, interface, Navier-Stokes equations, vacuum

CLC Number:

35Q30

Zhenhua Guo, Xueyao Zhang. INTERFACE BEHAVIOR AND DECAY RATES OF COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND A VACUUM^*[J].Acta mathematica scientia,Series B, 2024, 44(1): 247-274.

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INTERFACE BEHAVIOR AND DECAY RATES OF COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND A VACUUM^*

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