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

Yu Yu Bakhtin; E. I. Dinaburg; Ya G. Sinai

doi:10.1070/RM2004v059n06ABEH000795

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

Yu Yu Bakhtin, E. I. Dinaburg, Ya G. Sinai

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4 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1061-1078
Number of pages	18
Journal	Russian Mathematical Surveys
Volume	59
Issue number	6
DOIs	https://doi.org/10.1070/RM2004v059n06ABEH000795
State	Published - 2004

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1070/RM2004v059n06ABEH000795

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title = "On solutions with infinite energy and enstrophy of the Navier-Stokes system",

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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year = "2004",

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publisher = "Steklov Mathematical Institute of Russian Academy of Sciences",

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AU - Bakhtin, Yu Yu

AU - Dinaburg, E. I.

AU - Sinai, Ya G.

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N2 - 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.

AB - 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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U2 - 10.1070/RM2004v059n06ABEH000795

DO - 10.1070/RM2004v059n06ABEH000795

M3 - Article

AN - SCOPUS:17744380825

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VL - 59

SP - 1061

EP - 1078

JO - Russian Mathematical Surveys

JF - Russian Mathematical Surveys

IS - 6

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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