On solutions with infinite energy and enstrophy of the Navier-Stokes system

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© 2004 Russian Academy of Sciences, (DoM) and London Mathematical Society, Turpion Ltd
, , Citation Yu Yu Bakhtin et al 2004 Russ. Math. Surv. 59 1061 DOI 10.1070/RM2004v059n06ABEH000795

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1 International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow, Russian Federation

2 Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russian Federation

3 Mathematics Department, Princeton University, Princeton, New Jersey, United States of America

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0036-0279/59/6/1061

Abstract

The Cauchy problem is considered for the Navier-Stokes system. Local and global existence and uniqueness theorems are given for initial data whose Fourier transform decays at infinity as a power-law function with negative exponent and has a power-law singularity at zero. The paper contains a survey of known facts and some new results.

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10.1070/RM2004v059n06ABEH000795