Abstract
We study Navier-Stokes equations perturbed with a maximal monotone operator, in a bounded domain, in 2D and 3D. Using the theory of nonlinear semigroups, we prove existence results for strong and weak solutions. Examples are also provided.
Research Article | Open Access
Navier-Stokes Equations with Potentials
Academic Editor: Viorel Barbu
Received11 Mar 2007
Accepted08 May 2007
Published03 Jun 2007
References
P. Constantin and C. Foiaş, Navier-Stokes Equations, The University of Chicago Press, Chicago, Ill, USA, 1989.
View at: Google ScholarR. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, vol. 2 of Studies in Mathematics and Its Applications, North-Holland, Amsterdam, The Netherlands, 1979.
View at: Google Scholar | Zentralblatt MATH | MathSciNetR. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis, vol. 66 of CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 2nd edition, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNetV. Barbu and S. S. Sritharan, “Flow invariance preserving feedback controllers for the Navier-Stokes equation,” Journal of Mathematical Analysis and Applications, vol. 255, no. 1, pp. 281–307, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetV. Barbu, Analysis and Control of Nonlinear Infinite-Dimensional Systems, vol. 190 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1993.
View at: Google Scholar | Zentralblatt MATH | MathSciNetI. I. Vrabie, -Semigroups and Applications, vol. 191 of North-Holland Mathematics Studies, North-Holland, Amsterdam, The Netherlands, 2003.
View at: Google Scholar | MathSciNetV. Barbu, “The time optimal control of Navier-Stokes equations,” Systems & Control Letters, vol. 30, no. 2-3, pp. 93–100, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetH. Brézis, Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland Mathematics Studies, no. 5. Notas de Matemática (50), North-Holland, Amsterdam, The Netherlands, 1973.
View at: Google Scholar | Zentralblatt MATH | MathSciNetV. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei Republicii Socialiste România, Bucharest, Romania, 1976.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
Copyright
Copyright © 2007 Adriana-Ioana Lefter. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.