The global well-posedness of the multi-dimensional compressible Euler system with damping in the $L^p$ critical Besov spaces for $p<2$

TL;DR

This paper proves the global well-posedness of the multi-dimensional compressible Euler system with damping in critical Besov spaces for p<2, using new product estimates in hybrid Besov spaces.

Contribution

It introduces a novel product estimate in $L^2$-$L^p$ hybrid Besov spaces, enabling the analysis of the Euler system in critical spaces for p<2.

Findings

Global well-posedness in $L^p$-critical Besov spaces for 1≤p<2

Development of a new product estimate in hybrid Besov spaces

Extension of well-posedness results to multi-dimensional compressible Euler system with damping

Abstract

In this paper, we study the Cauchy's problem of the compressible Euler system with damping and establish the global-in-time well-posedness in $L^p$-type critical Besov spaces for $1\leq p<2$. To achieve it, a new product estimate is established in $L^2$-$L^p$ hybrid Besov spaces.