Publication Cover
Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 12
273
Views
40
CrossRef citations to date
0
Altmetric
Original Articles

The Navier–Stokes problem modified by an absorption term

&
Pages 1805-1825 | Received 16 Mar 2010, Accepted 17 May 2010, Published online: 21 Sep 2010

References

  • Serrin , J . 1959 . Mathematical Principles of Classical Fluid Mechanics, Handbuch der Physic Bd 8/1 , 125 – 263 . Berlin, Göttingen, Heidelberg : Springer-Verlag .
  • Temam , R . 2000 . Some Developments on Navier–Stokes Equations in the second half of the 20th Century, In: Development of Mathematics 1950–2000 , Edited by: Pier , J-P . 1049 – 1106 . Basel : Birkhäuser .
  • Wiegner , M . 1987 . Decay results for weak solutions of the Navier–Stokes equations on ℝ N . J. London Math. Soc. , 35 ( 2 ) : 303 – 313 .
  • Schonbek , ME . 1991 . Lower bounds of rates of decay for solutions to the Navier–Stokes equations . J. Amer. Math. Soc. , 4 ( 3 ) : 423 – 449 .
  • Borchers , W and Miyakawa , T . 1992 . L 2-Decay for Navier–Stokes flows in unbounded domains, with application to exterior stationary flows . Arch. Rational Mech. Anal. , 118 : 273 – 295 .
  • Kozono , H and Ogawa , T . 1993 . Decay properties of strong solutions for the Navier–Stokes equations in two-dimensional unbounded domains . Arch. Rational Mech. Anal. , 122 ( 1 ) : 1 – 17 .
  • Takahashi , S . 1999 . A weighted equation approach to decay rate estimates for the Navier–Stokes equations . Nonlinear Anal. , 37 : 751 – 789 .
  • Enomoto , Y and Shibata , Y . 2005 . On the rate of decay of the Oseen semigroup in exterior domains and its application to Navier–Stokes equation . J. Math. Fluid Mech. , 7 : 339 – 367 .
  • Bae , H-O and Jin , BJ . 2005 . Upper and lower bounds of temporal and spatial decays for the Navier–Stokes equations . J. Differ. Eqns. , 209 : 365 – 391 .
  • Antontsev , SN , Díaz , JI and Shmarev , SI . 2002 . Energy Methods for Free Boundary Problems, Progress in Nonlinear Differential Equations Applications , Vol. 48 , Boston : Birkhäuser .
  • Bae , H-O . 1999 . Existence, regularity, and decay rate of solutions of non-Newtonian flow . J. Math. Anal. Appl. , 231 ( 2 ) : 467 – 491 .
  • Benilan , Ph , Brezis , H and Crandall , MG . 1975 . A semilinear equation in L 1(R N ) . Ann. Scuola Norm. Sup. Pisa Cl. Sci. , 2 ( 4 ) : 523 – 555 .
  • Díaz , JI and Herrero , MA . 1981 . Estimates on the support of the solutions of some nonlinear elliptic and parabolic problems . Proc. Roy. Soc. Edinburgh Sect. A , 89 ( 3–4 ) : 249 – 258 .
  • Bernis , F . 1986 . Finite speed of propagation and asymptotic rates for some nonlinear higher order parabolic equations with absorption . Proc. Roy. Soc. Edinburgh Sect. A , 104 ( 1–2 ) : 1 – 19 .
  • Antontsev , SN and Oliveira , HB de . 1997 . Navier–Stokes equations with absorption under slip boundary conditions: Existence, uniqueness and extinction in time , 21 – 42 . Kyoto, , Japan : RIMS Kôkyûroku Bessatsu B1, University of Kyoto .
  • Lions , J-L . 1969 . Quelques Méthodes de Résolution des Problèmes aux Limites Non-linéaires , Paris : Dunod .
  • Galdi , GP . 2000 . “ An introduction to the Navier–Stokes initial-boundary value problem ” . In Fundamental Directions in Mathematical Fluid Mechanics , Edited by: Galdi , GP . 1 – 70 . Basel : Birkhäuser Verlag .
  • Ladyzhenskaya , OA , Solonnikov , VA and Uraltseva , NN . 1967 . Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs , Vol. 23 , Providence, RI : AMS .
  • Barret , JW and Liu , WB . 1994 . Finite element approximation of the parabolic p-Laplacian . SIAM J. Numer. Anal. , 31 ( 2 ) : 413 – 428 .
  • de Oliveira , HB . 2009 . “ On the influence of an absorption term in incompressible fluid flows ” . In Advances in Mathematical Fluid Mechanics , Edited by: Rannacher , R and Sequeira , A . 409 – 424 . New York : Springer-Verlag .
  • Antontsev , SN , Díaz , JI and de Oliveira , HB . 2004 . Stopping a viscous fluid by a feedback dissipative field. I. The stationary Stokes problem . J. Math. Fluid Mech. , 6 ( 4 ) : 439 – 461 .
  • Antontsev , SN , Díaz , JI and de Oliveira , HB . 2004 . Stopping a viscous fluid by a feedback dissipative field. II. The stationary Navier–Stokes problem . Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. , 15 ( 3–4 ) : 257 – 270 .

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.