A proof is proposed that small L1∩L2 initial data yields global classical solutions and optimal time-decay rates when the viscosity exponent α is within δ of 1.
Global large strong solutions to the compressible Navier-Stokes equations with density-dependent viscosities, case I: isentropic flows
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abstract
In this paper, we consider the Cauchy problem for the three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering the system as an elliptic-dominated structure and defining suitable energy functionals, after the elaborate index analysis, we establish the global existence of strong solutions as long as the initial data is large enough. This is a big contrast to the classical results where the initial data is a small perturbation of some resting states.
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Global existence and optimal time-decay rates of the compressible Navier-Stokes equations with density-dependent viscosities
A proof is proposed that small L1∩L2 initial data yields global classical solutions and optimal time-decay rates when the viscosity exponent α is within δ of 1.