Absence of the local existence theorem in the critical space for the 3D-Navier-Stokes system

Yakov Sinai

doi:10.1142/S0218127405014283

Absence of the local existence theorem in the critical space for the 3D-Navier-Stokes system

Yakov Sinai

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the 3D-Navier-Stokes System (NSS) on R³ without external forcing. After Fourier transform we get a nonlocal nonlinear integral equation equivalent to NSS. For one-parameter families of initial conditions A · c⁽⁰⁾(k)/|k|² in the case of small |A| the NSS has a unique global solution. We argue that for large A NSS has no local solutions with these initial conditions.

Original language	English (US)
Pages (from-to)	3635-3637
Number of pages	3
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	15
Issue number	11
DOIs	https://doi.org/10.1142/S0218127405014283
State	Published - Nov 2005

All Science Journal Classification (ASJC) codes

Modeling and Simulation
Engineering (miscellaneous)
General
Applied Mathematics

Keywords

Critical space
Fourier transform
Navier-Stokes system

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10.1142/S0218127405014283

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abstract = "We consider the 3D-Navier-Stokes System (NSS) on R3 without external forcing. After Fourier transform we get a nonlocal nonlinear integral equation equivalent to NSS. For one-parameter families of initial conditions A · c(0)(k)/|k|2 in the case of small |A| the NSS has a unique global solution. We argue that for large A NSS has no local solutions with these initial conditions.",

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AB - We consider the 3D-Navier-Stokes System (NSS) on R3 without external forcing. After Fourier transform we get a nonlocal nonlinear integral equation equivalent to NSS. For one-parameter families of initial conditions A · c(0)(k)/|k|2 in the case of small |A| the NSS has a unique global solution. We argue that for large A NSS has no local solutions with these initial conditions.

KW - Critical space

KW - Fourier transform

KW - Navier-Stokes system

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JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 11

ER -

Absence of the local existence theorem in the critical space for the 3D-Navier-Stokes system

Abstract

All Science Journal Classification (ASJC) codes

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