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三维带有衰减项的不可压缩Navier-Stokes方程组强解整体存在性和唯一性的研究

2021-01-05李凯

科技风 2021年35期
关键词:广汉方程组助教

参考文献:

[1]JEAN L.Sur le mouvement d'un liquid visqueux emplissant l'espace.Acta Math,63(1934):193-248.

[2]EBERHARD H.ber die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen.Math.Nachr,4(1951):213-231.

[3]LUIS A C,ROBERT K,LUIS N.Partial regularity of suitable weak solution of the Navier-Stokes equations.Comm.Pure Appl.Math,35(1982):771-831.

[4]ESCAURIAZA L,SEREGIN G A,SVERAK V.L,3-solutions of Navier-Stokes equations and backward uniqueness.Russian Math.Surveys,58(2003):211-250.

[5]GIGA Y.Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system.J.Differential Equations,62(1986):186-212.

[6]KATO T.Strong,Lp-solutions of the Navier-Stokes equation inRm,with applications to weak solutions.Math.Z,187(1984):635-658.

[7]LADYZHENSKAYA O A,SILVERMAN R A,SCHWARTZ J T,et al.The Mathematical Theory of Viscous Incompressible Flow.Gordon and Breach,New York,1969.

[8]LEMARé-RIEUSSET P G.Recent developments in the Navier-Stokes problem.Chapman&Hall/CRC,London,2002.

[9]P.L Lion.Mathematical Topics in Fluid Mechanics:Incompressible Models.Oxford Univ.Press,1996.

[10]J.Serrin.on the interior regularity of weak solutions of the Navier-Stokes equations.Arch.Ration.Mech.Anal,9(1962):187-195.

[11]H.Sohr.The Navier-Stokes Equations:An Elementary Functional Analytic Approach.Birkhuser,2001.

[12]M.Struwe.On partial regularity results for the Navier-Stokes equations.Comm.Pure Appl.Math,41(1998):437-458.

[13]R.Ternan.Navier——Stokes Equations,Theory and Numerical Analysis[J].Amsterdam:North—Holland,1977,1:984.

[14]C.Foias.Une remarque sur l'unicite des equations de Navier-Stokes en dimension n.Bull.Soc.Math.France,89(1961):1-8.

[15]K.Masuda.Weak solutions of the Navier-Stokes equations.Tohoku Math.J,36(1894):623-646.

[16]J.serrin.The initial value problem for the Navier-Stokes equations,in:R.Langer(Ed.).Nonlinear Problem,Wisconsin Univ.Press,1963.

[17]D.Bresch,B.Desjardins.Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model.Comm.Math.Phys,238(2003):211-223.

[18]D.Bresch,B.Desjardins,C.K.Lin.On some compressible fluid modles:Korteweg,lubrication,and shallow water systems,Comm.Partial Differential Equations,28(2003):843-868.

[19]L.Hsiao.Quasilinear Hyperbolic Systems and Dissipative Mechanisms.World Scientific,1997.

[20]F.M.Huang,R.H.Pan.Convergence rate for compressible Euler equations with damping and vacuum.Arch.Ration.Mech.Anal,166(2003):359-376.

[21]X.J.Cai,Q.S.Jiu.Weak and strong solutions for the incompressible Navier-Stokes equations with damping[J].Journal of Mathematical Analysis and Applications,2008,343(2):799-809.

[22]Zhang Z,Wu X,Lu M.On the uniqueness of strong solution to the incompressible Navier-Stokes equations with damping[J].Journal of Mathematical Analysis and Applications,2011,377(1):414-419.

[23]Zhou Y.Regularity and uniqueness for the 3D incompressible Navier-Stokes equations with damping[J].Applied Mathematics Letters,2012,25(11):1822-1825.

作者簡介:李凯(1992— ),男,汉族,四川广汉人,硕士,助教,研究方向:偏微分方程。

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