Remark on regularity of weak solutions to the Navier-Stokes equations

Zdeněk Skalák; Petr Kučera

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 1, page 111-117
  • ISSN: 0010-2628

Abstract

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Some results on regularity of weak solutions to the Navier-Stokes equations published recently in [3] follow easily from a classical theorem on compact operators. Further, weak solutions of the Navier-Stokes equations in the space L 2 ( 0 , T , W 1 , 3 ( 𝛺 ) 3 ) are regular.

How to cite

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Skalák, Zdeněk, and Kučera, Petr. "Remark on regularity of weak solutions to the Navier-Stokes equations." Commentationes Mathematicae Universitatis Carolinae 42.1 (2001): 111-117. <http://eudml.org/doc/22544>.

@article{Skalák2001,
abstract = {Some results on regularity of weak solutions to the Navier-Stokes equations published recently in [3] follow easily from a classical theorem on compact operators. Further, weak solutions of the Navier-Stokes equations in the space $L^2(0,T,W^\{1,3\}(\varOmega )^3)$ are regular.},
author = {Skalák, Zdeněk, Kučera, Petr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Navier-Stokes equations; weak solution; regularity; regularity of weak solutions to the Navier-Stokes equations; compact operators},
language = {eng},
number = {1},
pages = {111-117},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Remark on regularity of weak solutions to the Navier-Stokes equations},
url = {http://eudml.org/doc/22544},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Skalák, Zdeněk
AU - Kučera, Petr
TI - Remark on regularity of weak solutions to the Navier-Stokes equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 1
SP - 111
EP - 117
AB - Some results on regularity of weak solutions to the Navier-Stokes equations published recently in [3] follow easily from a classical theorem on compact operators. Further, weak solutions of the Navier-Stokes equations in the space $L^2(0,T,W^{1,3}(\varOmega )^3)$ are regular.
LA - eng
KW - Navier-Stokes equations; weak solution; regularity; regularity of weak solutions to the Navier-Stokes equations; compact operators
UR - http://eudml.org/doc/22544
ER -

References

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  1. Giga Y., Solutions for semilinear parabolic equations in L p and regularity of weak solutions of the Navier-Stokes system, J. Differential Equations 62 (1986), 182-212. (1986) MR0833416
  2. Kato T., Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Heidelberg, New York 1980. Zbl0836.47009
  3. Kozono H., Uniqueness and regularity of weak solutions to the Navier-Stokes equations, Lecture Notes in Num. and Appl. Anal. 16 (1998), 161-208. (1998) Zbl0941.35065MR1616331
  4. Neustupa J., Partial regularity of weak solutions to the Navier-Stokes Equations in the class L ∞ ( 0 , T , L 3 ( 𝛺 ) ) , J. Math. Fluid Mech. 1 (1999), 1-17. (1999) MR1738173
  5. Serrin J., On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal. 9 (1962), 187-195. (1962) Zbl0106.18302MR0136885
  6. Temam R., Navier-Stokes Equations, Theory and Numerical Analysis, North-Holland Publishing Company, Amsterdam, New York, Oxford, 1979. Zbl0981.35001MR0603444
  7. Temam R., Navier-Stokes Equations and Nonlinear Functional Analysis, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, second edition, 1995. Zbl0833.35110MR1318914

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