Regularity of pressure in the neighbourhood of regular points of weak solutions of the Navier-Stokes equations

Zdeněk Skalák; Petr Kučera

Applications of Mathematics (2003)

  • Volume: 48, Issue: 6, page 573-586
  • ISSN: 0862-7940

Abstract

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In the context of the weak solutions of the Navier-Stokes equations we study the regularity of the pressure and its derivatives in the space-time neighbourhood of regular points. We present some global and local conditions under which the regularity is further improved.

How to cite

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Skalák, Zdeněk, and Kučera, Petr. "Regularity of pressure in the neighbourhood of regular points of weak solutions of the Navier-Stokes equations." Applications of Mathematics 48.6 (2003): 573-586. <http://eudml.org/doc/33169>.

@article{Skalák2003,
abstract = {In the context of the weak solutions of the Navier-Stokes equations we study the regularity of the pressure and its derivatives in the space-time neighbourhood of regular points. We present some global and local conditions under which the regularity is further improved.},
author = {Skalák, Zdeněk, Kučera, Petr},
journal = {Applications of Mathematics},
keywords = {Navier-Stokes equations; regularity of weak solutions; regular and singular points; Navier-Stokes equations; regularity of weak solutions; regular and singular points},
language = {eng},
number = {6},
pages = {573-586},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Regularity of pressure in the neighbourhood of regular points of weak solutions of the Navier-Stokes equations},
url = {http://eudml.org/doc/33169},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Skalák, Zdeněk
AU - Kučera, Petr
TI - Regularity of pressure in the neighbourhood of regular points of weak solutions of the Navier-Stokes equations
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 6
SP - 573
EP - 586
AB - In the context of the weak solutions of the Navier-Stokes equations we study the regularity of the pressure and its derivatives in the space-time neighbourhood of regular points. We present some global and local conditions under which the regularity is further improved.
LA - eng
KW - Navier-Stokes equations; regularity of weak solutions; regular and singular points; Navier-Stokes equations; regularity of weak solutions; regular and singular points
UR - http://eudml.org/doc/33169
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. 10.2307/2372517, Amer. J.  Math. 78 (1956), 289–309. (1956) MR0084633DOI10.2307/2372517
  3. Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations, J.  Math. Pures Appl. 58 (1979), 339–368. (1979) MR0544257
  4. An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Vol. I: Linearized and Steady Problems; Vol. II: Nonlinear Steady Problems, Springer-Verlag, New York-Berlin-Heidelberg, 1994. (1994) MR1284205
  5. 10.1080/03605309808821374, Comm. Partial Differential Equations 23 (1998), 949–966. (1998) Zbl0910.35090MR1632780DOI10.1080/03605309808821374
  6. 10.1007/s000210050015, J.  Math. Fluid Mech. 1 (1999), 356–387. (1999) MR1738171DOI10.1007/s000210050015
  7. 10.1007/BF00253344, Arch. Rational Mech. Anal. 9 (1962), 187–195. (1962) Zbl0106.18302MR0136885DOI10.1007/BF00253344
  8. 10.1007/BF02677860, Manuscripta Math. 94 (1997), 365–384. (1997) Zbl0896.35106MR1485443DOI10.1007/BF02677860
  9. The Navier-Stokes Equations, Theory and Numerical Analysis, North-Holland Publishing Company, Amsterodam-New York-Oxford, 1979. (1979) MR0603444

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