LARGE GLOBAL SOLUTIONS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN THREE DIMENSIONS

摘要

This work concerns the initial value problem for the three dimen-sional compressible Navier-Stokes equations (both isentropic and polytropic). By exploiting the famous Fujita-Kato theorem to the Classical incompressible Navier-Stokes equations, we prove the existence of global-in-time unique solu-tions under as weak as possible smallness conditions in the scaling invariant spaces. In particular, our results improve the classical theorems obtained by Danchin [Invent. Math., 141, 579-614, 2000] and Danchin [Arch. Ration. Mech. Anal., 160, 1-39, 2001].

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