THE EXISTENCE OF GLOBAL SOLUTIONS FOR THE FULL NAVIER-STOKES-KORTEWEG SYSTEM OF VAN DER WAALS GAS∗

doi:10.1007/s10473-023-0201-9

Abstract

Abstract: The aim of this work is to prove the existence for the global solution of a non-isothermal or non-isentropic model of capillary compressible fluids derived by J. E. Dunn and J. Serrin (1985), in the case of van der Waals gas. Under the small initial perturbation, the proof of the global existence is based on an elementary energy method using the continuation argument of local solution. Moreover, the uniqueness of global solutions and large time behavior of the density are given. It is one of the main difficulties that the pressure $p$ is not the increasing function of the density $\rho$.

Key words: Navier-Stokes-Korteweg system, van der Waals gas, existence, uniqueness

Hakho Hong. THE EXISTENCE OF GLOBAL SOLUTIONS FOR THE FULL NAVIER-STOKES-KORTEWEG SYSTEM OF VAN DER WAALS GAS^∗[J].Acta mathematica scientia,Series B, 2023, 43(2): 469-491.

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THE EXISTENCE OF GLOBAL SOLUTIONS FOR THE FULL NAVIER-STOKES-KORTEWEG SYSTEM OF VAN DER WAALS GAS^∗

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