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



Hongjie Dong

Dong Li


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.


Spatial analyticity; bootstrap; Navier-Stokes equations

2010 Mathematics Subject Classification

35B65, 35Q30, 35Q35

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