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Weak and strong solutions for the incompressible Navier-Stokes equations with damping. (English) Zbl 1143.35349
Summary: We show that the Cauchy problem of the Navier-Stokes equations with damping α|u| β-1 u(α>0) has global weak solutions for any β1, global strong solution for any β7/2 and that the strong solution is unique for any 7/2β5.
35Q30Stokes and Navier-Stokes equations
76D05Navier-Stokes equations (fluid dynamics)
76D03Existence, uniqueness, and regularity theory
[1]Bresch, D.; Desjardins, B.: Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model, Comm. math. Phys. 238, No. 1 – 2, 211-223 (2003) · Zbl 1037.76012 · doi:10.1007/s00220-003-0859-8
[2]Bresch, D.; Desjardins, B.; Lin, Chi-Kun: On some compressible fluid models: Korteweg, lubrication, and shallow water systems, Comm. partial differential equations 28, No. 3 – 4, 843-868 (2003) · Zbl 1106.76436 · doi:10.1081/PDE-120020499
[3]Escauriaza, L.; Seregin, G.; Sverak, V.: On L3,-solutions to the Navier – Stokes equations and backward uniqueness, Russian math. Surveys 58, 211-250 (2003) · Zbl 1064.35134 · doi:10.1070/RM2003v058n02ABEH000609
[4]Foias, C.: Une remarque sur l’unicite des solutions des equations de Navier – Stokes en dimension n, Bull. soc. Math. France 89, 1-8 (1961) · Zbl 0107.07602 · doi:numdam:BSMF_1961__89__1_0
[5]Giga, Y.: Solutions for semilinear parabolic equations in lp and regularity of weak solutions of the Navier – Stokes system, J. differential equations 61, 186-212 (1986) · Zbl 0577.35058 · doi:10.1016/0022-0396(86)90096-3
[6]Hopf, E.: Über die anfangswertaufgabe für die hydrody namischen grundgleichungen, Math. nachr. 4, 213-231 (1951) · Zbl 0042.10604
[7]Hsiao, L.: Quasilinear hyperbolic systems and dissipative mechanisms, (1997) · Zbl 0911.35003
[8]Huang, F. M.; Pan, R. H.: Convergence rate for compressible Euler equations with damping and vacuum, Arch. ration. Mech. anal. 166, 359-376 (2003) · Zbl 1022.76042 · doi:10.1007/s00205-002-0234-5
[9]Kato, T.: Strong lp solutions of the Navier – Stokes equations in rn, with application to weak solutions, Math. Z. 187, 471-480 (1984) · Zbl 0545.35073 · doi:10.1007/BF01174182
[10]Ladyzhenskaya, O. A.: The mathematical theory of viscous incompressible flow, (1969) · Zbl 0184.52603
[11]Leray, J.: Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta math. 63, 193-248 (1934) · Zbl 60.0726.05 · doi:10.1007/BF02547354
[12]Lions, P. L.: Mathematical topics in fluid mechanics: incompressible models, (1996)
[13]Masuda, K.: Weak solutions of the Navier – Stokes equations, Tohoku math. J. 36, 623-646 (1984) · Zbl 0568.35077 · doi:10.2748/tmj/1178228767
[14]Serrin, J.: On the interior regularity of weak solutions of the Navier – Stokes equations, Arch. ration. Mech. anal. 9, 187-195 (1962) · Zbl 0106.18302 · doi:10.1007/BF00253344
[15]Serrin, J.: The initial value problem for the Navier – Stokes equations, Nonlinear problem (1963) · Zbl 0115.08502
[16]Sohr, H.: The Navier – Stokes equations: an elementary functional analytic approach, (2001)
[17]Struwe, M.: On partial regularity results for the Navier – Stokes equations, Comm. pure appl. Math. 41, 437-458 (1988) · Zbl 0632.76034 · doi:10.1002/cpa.3160410404
[18]Temam, R.: Navier – Stokes equations theory and numerical analysis, (1984)