Compressible Navier–Stokes equations without heat conduction in $$L^p$$ -framework

Abstract

In this paper, we mainly consider global well-posedness and long time behavior of compressible Navier–Stokes equations without heat conduction in \(L^p\)-framework. This is a generalization of Peng and Zhai (SIMA 55(2):1439–1463, 2023), where they obtained the corresponding result in \(L^2\)-framework. Based on the key observation that we can release the regularity of non-dissipative entropy S in high frequency in Peng and Zhai (2023), we ultimately achieve the desired \(L^p\) estimate in the high frequency via complicated calculations on the nonlinear terms. In addition, we get the \(L^p\)-decay rate of the solution.