Global existence of strong solutions to the 3D isentropic compressible Navier–Stokes equations with density‐dependent viscosities

摘要

We consider the Cauchy problem to the three‐dimensional isentropic compressible Navier–Stokes system with density‐dependent viscosities. Under the condition that the lower bound of initial density is sufficiently large, we prove that strong solutions exist globally in time. The initial data can be arbitrarily large.