Global large solution to the compressible Navier-Stokes equations in critical Besov space ${\dot{B}}_{\infty ,\infty }^{-1}$

Abstract

In this paper, we construct a class of global large solution to the compressible Navier-Stokes equations in the whole space ${\mathbb{R}}^d$. Precisely speaking, our choice of special initial data whose ${\dot{B}}_{\infty ,\infty }^{-1}$ norm can be arbitrarily large, namely, $||u_0|{|}_{{\dot{B}}_{\infty ,\infty }^{-1}}\gg 1$, allows to give rise to global-in-time solution to the compressible Navier-Stokes equations.

References in corpus (2)

• Structure of Helicity and Global Solutions of Incompressible Navier-Stokes Equation
• A class large solution of the 2D MHD equations with velocity and magnetic damping