LONG TIME EXISTENCE FOR THE NON-ISENTROPIC SLIGHTLY COMPRESSIBLE FLUID MODEL OF KORTEWEG TYPE

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doi:10.1007/s10473-025-0209-4

Abstract: We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system. Under the conditions of slight density and temperature variations, we verify that the full compressible Navier-Stokes-Korteweg equations admit a unique strong solution as long as the solution of the limiting system exists, when the Mach number is sufficiently small. Furthermore, we deduce the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on the time interval in which the solution exists.

Key words: non-isentropic compressible Navier-Stokes-Korteweg equations, low Mach number limit, long time existence, strong solution

CLC Number:

35D35

Qiangchang Ju, Jianjun Xu. LONG TIME EXISTENCE FOR THE NON-ISENTROPIC SLIGHTLY COMPRESSIBLE FLUID MODEL OF KORTEWEG TYPE[J].Acta mathematica scientia,Series B, 2025, 45(2): 416-445.

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