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

Commentationes Mathematicae Universitatis Carolinae (2001)

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

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topSkalák, 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

top- 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) Zbl0577.35058MR0833416
- Kato T., Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Heidelberg, New York 1980. Zbl0836.47009
- 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
- Neustupa J., Partial regularity of weak solutions to the Navier-Stokes Equations in the class ${L}^{\infty}(0,T,{L}^{3}\left(\mathit{\Omega}\right))$, J. Math. Fluid Mech. 1 (1999), 1-17. (1999) Zbl0949.35107MR1738173
- 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
- Temam R., Navier-Stokes Equations, Theory and Numerical Analysis, North-Holland Publishing Company, Amsterdam, New York, Oxford, 1979. Zbl0981.35001MR0603444
- 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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