A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations

Neustupa, Jiří. "A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations." Mathematica Bohemica 139.4 (2014): 685-698. <http://eudml.org/doc/269831>.

@article{Neustupa2014,
abstract = {We deal with a suitable weak solution $(\mathbf \{v\},p)$ to the Navier-Stokes equations in a domain $\Omega \subset \mathbb \{R\}^3$. We refine the criterion for the local regularity of this solution at the point $(\mathbf \{f\}x_0,t_0)$, which uses the $L^3$-norm of $\mathbf \{v\}$ and the $L^\{3/2\}$-norm of $p$ in a shrinking backward parabolic neighbourhood of $(\mathbf \{x\}_0,t_0)$. The refinement consists in the fact that only the values of $\mathbf \{v\}$, respectively $p$, in the exterior of a space-time paraboloid with vertex at $(\mathbf \{x\}_0,t_0)$, respectively in a ”small” subset of this exterior, are considered. The consequence is that a singularity cannot appear at the point $(\mathbf \{x\}_0,t_0)$ if $\mathbf \{v\}$ and $p$ are “smooth” outside the paraboloid.},
author = {Neustupa, Jiří},
journal = {Mathematica Bohemica},
keywords = {Navier-Stokes equation; suitable weak solution; regularity; Navier-Stokes equation; suitable weak solution; regularity},
language = {eng},
number = {4},
pages = {685-698},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations},
url = {http://eudml.org/doc/269831},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Neustupa, Jiří
TI - A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 4
SP - 685
EP - 698
AB - We deal with a suitable weak solution $(\mathbf {v},p)$ to the Navier-Stokes equations in a domain $\Omega \subset \mathbb {R}^3$. We refine the criterion for the local regularity of this solution at the point $(\mathbf {f}x_0,t_0)$, which uses the $L^3$-norm of $\mathbf {v}$ and the $L^{3/2}$-norm of $p$ in a shrinking backward parabolic neighbourhood of $(\mathbf {x}_0,t_0)$. The refinement consists in the fact that only the values of $\mathbf {v}$, respectively $p$, in the exterior of a space-time paraboloid with vertex at $(\mathbf {x}_0,t_0)$, respectively in a ”small” subset of this exterior, are considered. The consequence is that a singularity cannot appear at the point $(\mathbf {x}_0,t_0)$ if $\mathbf {v}$ and $p$ are “smooth” outside the paraboloid.
LA - eng
KW - Navier-Stokes equation; suitable weak solution; regularity; Navier-Stokes equation; suitable weak solution; regularity
UR - http://eudml.org/doc/269831
ER -