Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 1
145
Views
9
CrossRef citations to date
0
Altmetric
Articles

Remarks on regularity criterion for weak solutions to the Navier–Stokes equations in terms of the gradient of the pressure

Pages 96-103 | Received 30 Jul 2010, Accepted 20 May 2011, Published online: 07 Jul 2011

References

  • Leray , J . 1934 . Sur le mouvement d'un liquide visqueux emplissant l'espace . Acta Math. , 63 : 193 – 248 .
  • Hopf , E . 1951 . Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen . Math. Nachr. , 4 : 213 – 231 .
  • Chae , D and Lee , J . 2001 . Regularity criterion in terms of pressure for the Navier–Stokes equations . Nonlinear Anal. , 46 : 727 – 735 .
  • Caffarelli , L , Kohn , J and Nirenberg , L . 1982 . Partial regularity for suitable weak solutions of the Navier–Stokes equations . Commun. Pure Appl. Math. , 35 : 771 – 831 .
  • Serrin , J . 1962 . On the interior regularity of weak solutions of the Navier–Stokes equations . Arch. Rational. Mech. Anal. , 9 : 187 – 195 .
  • Giga , Y . 1986 . Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier–Stokes system . J. Differ. Eqns , 62 : 186 – 212 .
  • Struwe , M . 1988 . On partial regularity results for the Navier–Stokes equations . Commun. Pure Appl. Math. , 41 : 437 – 458 .
  • Struwe , M . 2007 . On a Serrin-type regularity criterion for the navier–stokes equations in terms of the pressure . J. Math. Fluid Mech. , 9 : 235 – 242 .
  • Zhou , Y . 2006 . On a regularity criterion in terms of the gradient of pressure for the Navier–Stokes equations in ℝn . Z. Angew. Math. Phys. , 57 : 384 – 392 .
  • Beirão da Veiga , H . 2000 . A sufficient condition on the pressure for the regularity of weak solutions to the Navier–Stokes equations . J. Math. Fluid Mech. , 2 : 99 – 106 .
  • Kozono , H and Sohr , H . 1997 . Regularity criterion on weak solutions to the Navier–Stokes equations . Adv. Differ. Eqns , 2 : 535 – 554 .
  • Sohr , H . 2001 . The Navier–Stokes Equations, An Elementary Functional Analytic Approach , Birkhäuser, Basel : Birkhäuser Advanced Texts .
  • Sohr , H and von Wahl , W . 1986 . On the regularity of the pressure of weak solutions of Navier–Stokes equations . Arch. Math. , 46 : 428 – 439 .
  • Kaniel , S . 1968 . A sufficient condition for smoothness of solutions of Navier–Stokes equations . Israel J. Math. , 6 : 354 – 358 .
  • Berselli , LC and Galdi , GP . 2002 . Regularity criteria involving the pressure for the weak solutions to the Navier–Stokes equations . Proc. Am. Math. Soc. , 130 : 3585 – 3595 .
  • Zhou , Y . 2004 . Regularity criteria in terms of pressure for the 3-D Navier–Stokes equations in a generic domain . Math. Ann. , 328 : 173 – 192 .
  • Zhou , Y . 2006 . On regularity criteria in terms of pressure for the Navier–Stokes equations in ℝ3 . Proc. Am. Math. Soc. , 134 : 149 – 156 .
  • Fan , J , Jiang , S and Ni , G . 2008 . On regularity criteria for the n-dimensional Navier–Stokes equations in terms of the pressure . J. Differ. Eqns , 244 : 2963 – 2979 .
  • Benbernou , S . 2009 . A note on the regularity criterion in terms of pressure for the Navier–Stokes equations . Appl. Math. Lett. , 22 : 1438 – 1443 .
  • Zhou , Y and Gala , S . 2011 . Regularity criteria in terms of the pressure for the Navier–Stokes equations in the critical Morrey–Campanato space . Z. Anal. Anwend. , 30 ( 1 ) : 83 – 93 .
  • Fan , J and Ozawa , Y . 2008 . Regularity criterion for weak solutions to the Navier–Stokes equations in terms of the gradient of the pressure . J. Ineq. Appl. , 2008 : 1 – 6 .
  • Gala , S . 2008 . Regularity criterion on weak solutions to the Navier–Stokes equations . J. Korean Math. Soc. , 45 : 537 – 558 .
  • Gala , S and Lemarié-Rieusset , PG . 2006 . Multipliers between Sobolev spaces and fractional differentiation . J. Math. Anal. Appl. , 322 : 1030 – 1054 .
  • Zhou , Y and Gala , S . 2009 . Logarithmically improved regularity criteria for the Navier–Stokes equations in multiplier spaces . J. Math. Anal. Appl. , 356 : 498 – 501 .
  • Kato , T . 1984 . Strong Lp-solutions of the Navier–Stokes equation in ℝm, with applications to weak solutions . Math. Z. , 187 : 471 – 480 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.