Global solutions of 2D isentropic compressible Navier-Stokes equations with one slow variable

TL;DR

This paper proves the global existence of smooth solutions to 2D isentropic compressible Navier-Stokes equations with initial data that vary slowly in one direction and are away from vacuum, including some non-perturbative cases.

Contribution

It establishes the global well-posedness for a class of initial data that are not small perturbations, extending previous results to more general initial conditions.

Findings

Global smooth solutions exist for the specified initial data.

Examples of initial data leading to unique solutions are provided.

Solutions are valid even when initial data are not small perturbations.

Abstract

Motivated by \cite{CG10,CZ6}, we prove the global existence of solutions to the two-dimensional isentropic compressible Navier-Stokes equations with smooth initial data which are slowly varying in one direction and with initial density being away from vacuum. In particular, we present examples of initial data which generate unique global smooth solutions to 2D compressible Navier-Stokes equations with constant viscosity and with initial data which are neither small perturbation of some constant equilibrium state nor of small energy.