THE GLOBAL EXISTENCE OF STRONG SOLUTIONS FOR A NON-ISOTHERMAL IDEAL GAS SYSTEM

doi:10.1007/s10473-024-0306-9

Abstract

Abstract: We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach. We first show the global well-posedness in the Sobolev space $H^{2}\left(\mathbb{R}^{3}\right)$ for solutions near equilibrium through iterated energy-type bounds and a continuity argument. We then prove the global well-posedness in the critical Besov space $\dot{B}_{2,1}^{3 / 2}$ by showing that the linearized operator is a contraction mapping under the right circumstances.

Key words: thermal fluid equations, energy-variational method, well-posedness theory for PDE, paraproduct calculus

CLC Number:

35A01

Bin Han, Ningan Lai, Andrei Tarfulea. THE GLOBAL EXISTENCE OF STRONG SOLUTIONS FOR A NON-ISOTHERMAL IDEAL GAS SYSTEM[J].Acta mathematica scientia,Series B, 2024, 44(3): 865-886.

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