Additional note on partial regularity of weak solutions of the Navier-Stokes equations in the class L ∞ ( 0 , T , L 3 ( Ω ) 3 )

Zdeněk Skalák

Applications of Mathematics (2003)

  • Volume: 48, Issue: 2, page 153-159
  • ISSN: 0862-7940

Abstract

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We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution 𝐮 belongs to L ∞ ( 0 , T , L 3 ( Ω ) 3 ) , then the set of all possible singular points of 𝐮 in Ω is at most finite at every time t 0 ∈ ( 0 , T ) .

How to cite

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Skalák, Zdeněk. "Additional note on partial regularity of weak solutions of the Navier-Stokes equations in the class $L^\infty (0,T,L^3(\Omega )^3)$." Applications of Mathematics 48.2 (2003): 153-159. <http://eudml.org/doc/33141>.

@article{Skalák2003,
abstract = {We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution $\{\mathbf \{u\}\}$ belongs to $L^\infty (0,T,L^3(\Omega )^3)$, then the set of all possible singular points of $\{\mathbf \{u\}\}$ in $\Omega $ is at most finite at every time $t_0\in (0,T)$.},
author = {Skalák, Zdeněk},
journal = {Applications of Mathematics},
keywords = {Navier-Stokes equations; partial regularity; Navier-Stokes equations; partial regularity},
language = {eng},
number = {2},
pages = {153-159},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Additional note on partial regularity of weak solutions of the Navier-Stokes equations in the class $L^\infty (0,T,L^3(\Omega )^3)$},
url = {http://eudml.org/doc/33141},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Skalák, Zdeněk
TI - Additional note on partial regularity of weak solutions of the Navier-Stokes equations in the class $L^\infty (0,T,L^3(\Omega )^3)$
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 2
SP - 153
EP - 159
AB - We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution ${\mathbf {u}}$ belongs to $L^\infty (0,T,L^3(\Omega )^3)$, then the set of all possible singular points of ${\mathbf {u}}$ in $\Omega $ is at most finite at every time $t_0\in (0,T)$.
LA - eng
KW - Navier-Stokes equations; partial regularity; Navier-Stokes equations; partial regularity
UR - http://eudml.org/doc/33141
ER -

References

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  1. 10.1002/cpa.3160350604, Comm. Pure Appl. Math. 35 (1982), 771–831. (1982) MR0673830DOI10.1002/cpa.3160350604
  2. Uniqueness and regularity of weak solutions to the Navier-Stokes equations, Lecture Notes Numer. Appl. Anal. 16 (1998), 161–208. (1998) Zbl0941.35065MR1616331
  3. 10.1524/anly.1996.16.3.255, Analysis 16 (1996), 255–271. (1996) MR1403221DOI10.1524/anly.1996.16.3.255
  4. 10.1007/s000210050013, J. Math. Fluid Mech. 1 (1999), 309–325. (1999) MR1738173DOI10.1007/s000210050013
  5. 10.1007/BF02677860, Manuscripta Math. 94 (1997), 365–384. (1997) MR1485443DOI10.1007/BF02677860
  6. Navier-Stokes Equations, North-Holland, Amsterdam-New York-Oxford, 1977. (1977) Zbl0383.35057MR0769654

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