Compressible Navier–Stokes equations without heat conduction in \(L^p\)-framework

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