Global well-posedness and optimal decay rates are established for the 3D barotropic compressible Navier-Stokes equations with a potential force, for initial data small in homogeneous Sobolev and Besov norms but with arbitrarily large L2 norm.
Brandolese, Characterization of solutions to dissipative systems with sharp algebraic decay,SIAM J
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Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data
Global well-posedness and optimal decay rates are established for the 3D barotropic compressible Navier-Stokes equations with a potential force, for initial data small in homogeneous Sobolev and Besov norms but with arbitrarily large L2 norm.