On a method of holomorphic functions to obtain sharp regularization rates of weak solutions of Navier-Stokes equations

We show that $L^2$ energy estimates combined with Cauchy integral formula for holomorphic functions can provide bounds for higher-order derivatives of smooth solutions of Navier-Stokes equations. We then extend this principle to weak solutions to improve regularization rates obtained by standard energy methods.

Keywords

Compressible Navier-Stokes equations, weak solutions, time analyticity, holomorphic functions

2010 Mathematics Subject Classification

Primary 35B35. Secondary 35B40, 76N10.

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Published 1 January 2007