Global solutions to the 3D compressible Navier–Stokes equations with a class of special initial data

Abstract

In this paper, we consider the Cauchy problem of tri-dimensional compressible Navier–Stokes equations and construct global smooth solutions by choosing a class of new special initial velocity and density whose [Formula: see text]-norm can be arbitrarily large and improve the previous result in Li et al. [J. Math. Fluid Mech. 24, 22 (2022)]. Our main idea is splitting the linearized equations from the compressible Navier–Stokes equations and exploring the damping effect of the linearized system.