GLOBAL WELL-POSEDNESS FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

doi:10.1007/s10473-022-0523-z

Abstract

Abstract: We are concerned with the Cauchy problem regarding the full compressible Navier-Stokes equations in $\mathbb{R}^d$ (d = 2, 3). By exploiting the intrinsic structure of the equations and using harmonic analysis tools (especially the Littlewood-Paley theory), we prove the global solutions to this system with small initial data restricted in the Sobolev spaces. Moreover, the initial temperature may vanish at infinity.

Key words: compressible Navier-Stokes equations, global well-posedness, Friedrich’s method, compactness arguments

CLC Number:

35Q35

Jinlu LI, Zhaoyang YIN, Xiaoping ZHAI. GLOBAL WELL-POSEDNESS FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS[J].Acta mathematica scientia,Series B, 2022, 42(5): 2131-2148.

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