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Navier-Stokes equations with potentials. (English) Zbl 1141.35433

Summary: 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.

MSC:

35Q30 Navier-Stokes equations
47N20 Applications of operator theory to differential and integral equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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References:

[1] P. Constantin and C. Foia\cs, Navier-Stokes Equations, The University of Chicago Press, Chicago, Ill, USA, 1989.
[2] R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, vol. 2 of Studies in Mathematics and Its Applications, North-Holland, Amsterdam, The Netherlands, 1979. · Zbl 0426.35003
[3] R. 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. · Zbl 0833.35110
[4] V. 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. · Zbl 1073.93030 · doi:10.1006/jmaa.2000.7256
[5] V. Barbu, Analysis and Control of Nonlinear Infinite-Dimensional Systems, vol. 190 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1993. · Zbl 0776.49005
[6] I. I. Vrabie, C0-Semigroups and Applications, vol. 191 of North-Holland Mathematics Studies, North-Holland, Amsterdam, The Netherlands, 2003. · Zbl 1119.47044
[7] V. Barbu, “The time optimal control of Navier-Stokes equations,” Systems & Control Letters, vol. 30, no. 2-3, pp. 93-100, 1997. · Zbl 0898.49011 · doi:10.1016/S0167-6911(96)00083-7
[8] H. 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. · Zbl 0252.47055
[9] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei Republicii Socialiste România, Bucharest, Romania, 1976. · Zbl 0328.47035
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