Communications in Mathematical Sciences

Volume 7 (2009)

Number 1

Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations

Pages: 67 – 80

DOI: http://dx.doi.org/10.4310/CMS.2009.v7.n1.a3

Authors

Hongjie Dong

Dong Li

Abstract

By using a new bilinear estimate, a pointwise estimate of the generalized Oseen kernel, and an idea of a fractional bootstrap, we establish optimal local smoothing and decay estimates of solutions to the Navier-Stokes equations with fractional dissipation. We also show that solutions are analytic in space variables.

Keywords

Spatial analyticity; bootstrap; Navier-Stokes equations

2010 Mathematics Subject Classification

35B65, 35Q30, 35Q35

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