Uniqueness of weak solutions of the Navier-Stokes equations

Sadek Gala

Applications of Mathematics (2008)

  • Volume: 53, Issue: 6, page 561-582
  • ISSN: 0862-7940

Abstract

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Consider the Navier-Stokes equation with the initial data a ∈ L σ 2 ( ℝ d ) . Let u and v be two weak solutions with the same initial value a . If u satisfies the usual energy inequality and if ∇ v ∈ L 2 ( ( 0 , T ) ; X ˙ 1 ( ℝ d ) d ) where X ˙ 1 ( ℝ d ) is the multiplier space, then we have u = v .

How to cite

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Gala, Sadek. "Uniqueness of weak solutions of the Navier-Stokes equations." Applications of Mathematics 53.6 (2008): 561-582. <http://eudml.org/doc/37801>.

@article{Gala2008,
abstract = {Consider the Navier-Stokes equation with the initial data $a\in L_\{\sigma \}^2( \mathbb \{R\}^d) $. Let $u$ and $v$ be two weak solutions with the same initial value $a$. If $u$ satisfies the usual energy inequality and if $\nabla v\in L^2(( 0,T) ;\dot\{X\} _1(\mathbb \{R\}^d)^d)$ where $\dot\{X\}_1(\mathbb \{R\}^d)$ is the multiplier space, then we have $u=v$.},
author = {Gala, Sadek},
journal = {Applications of Mathematics},
keywords = {Navier-Stokes equations; solution uniqueness; weak Leray-Hopf solution; multiplier space; Navier-Stokes equations; solution uniqueness; weak Leray-Hopf solution; multiplier space},
language = {eng},
number = {6},
pages = {561-582},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Uniqueness of weak solutions of the Navier-Stokes equations},
url = {http://eudml.org/doc/37801},
volume = {53},
year = {2008},
}

TY - JOUR
AU - Gala, Sadek
TI - Uniqueness of weak solutions of the Navier-Stokes equations
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 6
SP - 561
EP - 582
AB - Consider the Navier-Stokes equation with the initial data $a\in L_{\sigma }^2( \mathbb {R}^d) $. Let $u$ and $v$ be two weak solutions with the same initial value $a$. If $u$ satisfies the usual energy inequality and if $\nabla v\in L^2(( 0,T) ;\dot{X} _1(\mathbb {R}^d)^d)$ where $\dot{X}_1(\mathbb {R}^d)$ is the multiplier space, then we have $u=v$.
LA - eng
KW - Navier-Stokes equations; solution uniqueness; weak Leray-Hopf solution; multiplier space; Navier-Stokes equations; solution uniqueness; weak Leray-Hopf solution; multiplier space
UR - http://eudml.org/doc/37801
ER -

References

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