메뉴 건너뛰기




Volumn 93, Issue 6, 2010, Pages 559-571

Global well posedness for the Maxwell-Navier-Stokes system in 2D

Author keywords

Global well posedness; Maxwell equations; MHD; Navier Stokes equations

Indexed keywords


EID: 77953121044     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2009.08.007     Document Type: Article
Times cited : (80)

References (33)
  • 1
    • 48949084051 scopus 로고    scopus 로고
    • Résultats d'existence dans des espaces critiques pour le système de la MHD inhomogène
    • Abidi H., Hmidi T. Résultats d'existence dans des espaces critiques pour le système de la MHD inhomogène. Ann. Math. Blaise Pascal 2007, 14(1):103-148.
    • (2007) Ann. Math. Blaise Pascal , vol.14 , Issue.1 , pp. 103-148
    • Abidi, H.1    Hmidi, T.2
  • 2
    • 50849116761 scopus 로고    scopus 로고
    • Global weak solutions to equations of motion for magnetic fluids
    • Amirat Y., Hamdache K., Murat F. Global weak solutions to equations of motion for magnetic fluids. J. Math. Fluid Mech. 2008, 10(3):326-351.
    • (2008) J. Math. Fluid Mech. , vol.10 , Issue.3 , pp. 326-351
    • Amirat, Y.1    Hamdache, K.2    Murat, F.3
  • 3
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-D Euler equations
    • Beale J.T., Kato T., Majda A. Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Comm. Math. Phys. 1984, 94(1):61-66.
    • (1984) Comm. Math. Phys. , vol.94 , Issue.1 , pp. 61-66
    • Beale, J.T.1    Kato, T.2    Majda, A.3
  • 4
    • 0038368243 scopus 로고
    • Nonlinear Magnetohydrodynamics
    • Cambridge University Press, Cambridge
    • Biskamp D. Nonlinear Magnetohydrodynamics. Cambridge Monographs on Plasma Physics 1993, vol. 1. Cambridge University Press, Cambridge.
    • (1993) Cambridge Monographs on Plasma Physics , vol.1
    • Biskamp, D.1
  • 5
    • 0001191104 scopus 로고
    • Calcul symbolique propagation des singularités pour les équations aux dérivées partielles non linéaires
    • Bony J.-M. Calcul symbolique propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Sci. École Norm. Sup. (4) 1981, 14(2):209-246.
    • (1981) Ann. Sci. École Norm. Sup. (4) , vol.14 , Issue.2 , pp. 209-246
    • Bony, J.-M.1
  • 6
    • 34250744869 scopus 로고    scopus 로고
    • A losing estimate for the ideal MHD equations with application to blow-up criterion
    • (electronic)
    • Cannone M., Chen Q., Miao C. A losing estimate for the ideal MHD equations with application to blow-up criterion. SIAM J. Math. Anal. 2007, 38(6):1847-1859. (electronic).
    • (2007) SIAM J. Math. Anal. , vol.38 , Issue.6 , pp. 1847-1859
    • Cannone, M.1    Chen, Q.2    Miao, C.3
  • 7
    • 0003312241 scopus 로고
    • Fluides parfaits incompressibles
    • Chemin J.-Y. Fluides parfaits incompressibles. Astérisque 1995, 230:177.
    • (1995) Astérisque , vol.230 , pp. 177
    • Chemin, J.-Y.1
  • 8
    • 58149362915 scopus 로고
    • Flot de champs de vecteurs non lipschitziens équations de Navier-Stokes
    • Chemin J.-Y., Lerner N. Flot de champs de vecteurs non lipschitziens équations de Navier-Stokes. J. Differential Equations 1995, 121(2):314-328.
    • (1995) J. Differential Equations , vol.121 , Issue.2 , pp. 314-328
    • Chemin, J.-Y.1    Lerner, N.2
  • 9
    • 0035527616 scopus 로고    scopus 로고
    • About lifespan of regular solutions of equations related to viscoelastic fluids
    • (electronic)
    • Chemin J.-Y., Masmoudi N. About lifespan of regular solutions of equations related to viscoelastic fluids. SIAM J. Math. Anal. 2001, 33(1):84-112. (electronic).
    • (2001) SIAM J. Math. Anal. , vol.33 , Issue.1 , pp. 84-112
    • Chemin, J.-Y.1    Masmoudi, N.2
  • 10
    • 38049042966 scopus 로고    scopus 로고
    • Global well-posedness for a Smoluchowski equation coupled with Navier-Stokes equations in 2D
    • Constantin P., Masmoudi N. Global well-posedness for a Smoluchowski equation coupled with Navier-Stokes equations in 2D. Comm. Math. Phys. 2008, 278(1):179-191.
    • (2008) Comm. Math. Phys. , vol.278 , Issue.1 , pp. 179-191
    • Constantin, P.1    Masmoudi, N.2
  • 11
    • 0004213645 scopus 로고    scopus 로고
    • An Introduction to Magnetohydrodynamics
    • Cambridge University Press, Cambridge
    • Davidson P.A. An Introduction to Magnetohydrodynamics. Cambridge Texts in Applied Mathematics 2001, Cambridge University Press, Cambridge.
    • (2001) Cambridge Texts in Applied Mathematics
    • Davidson, P.A.1
  • 12
    • 0036812186 scopus 로고    scopus 로고
    • On the inviscid and non-resistive limit for the equations of incompressible magnetohydrodynamics
    • Díaz J.I., Lerena M.B. On the inviscid and non-resistive limit for the equations of incompressible magnetohydrodynamics. Math. Models Methods Appl. Sci. 2002, 12(10):1401-1419.
    • (2002) Math. Models Methods Appl. Sci. , vol.12 , Issue.10 , pp. 1401-1419
    • Díaz, J.I.1    Lerena, M.B.2
  • 13
    • 0015483298 scopus 로고
    • Inéquations en thermoélasticité magnétohydrodynamique
    • Duvaut G., Lions J.-L. Inéquations en thermoélasticité magnétohydrodynamique. Arch. Rational Mech. Anal. 1972, 46:241-279.
    • (1972) Arch. Rational Mech. Anal. , vol.46 , pp. 241-279
    • Duvaut, G.1    Lions, J.-L.2
  • 15
    • 52449103809 scopus 로고    scopus 로고
    • Remark on the regularity for weak solutions to the magnetohydrodynamic equations
    • He C., Wang Y. Remark on the regularity for weak solutions to the magnetohydrodynamic equations. Math. Methods Appl. Sci. 2008, 31(14):1667-1684.
    • (2008) Math. Methods Appl. Sci. , vol.31 , Issue.14 , pp. 1667-1684
    • He, C.1    Wang, Y.2
  • 16
    • 33749341214 scopus 로고    scopus 로고
    • Global solutions for a semilinear two-dimensional Klein-Gordon equation with exponential-type nonlinearity
    • Ibrahim S., Majdoub M., Masmoudi N. Global solutions for a semilinear two-dimensional Klein-Gordon equation with exponential-type nonlinearity. Comm. Pure Appl. Math. 2006, 59(11):1639-1658.
    • (2006) Comm. Pure Appl. Math. , vol.59 , Issue.11 , pp. 1639-1658
    • Ibrahim, S.1    Majdoub, M.2    Masmoudi, N.3
  • 17
    • 70350047372 scopus 로고    scopus 로고
    • Double logarithmic inequality with a sharp constant
    • (electronic)
    • Ibrahim S., Majdoub M., Masmoudi N. Double logarithmic inequality with a sharp constant. Proc. Amer. Math. Soc. 2007, 135(1):87-97. (electronic).
    • (2007) Proc. Amer. Math. Soc. , vol.135 , Issue.1 , pp. 87-97
    • Ibrahim, S.1    Majdoub, M.2    Masmoudi, N.3
  • 18
    • 0012945781 scopus 로고    scopus 로고
    • The critical Sobolev inequalities in Besov spaces regularity criterion to some semi-linear evolution equations
    • Kozono H., Ogawa T., Taniuchi Y. The critical Sobolev inequalities in Besov spaces regularity criterion to some semi-linear evolution equations. Math. Z. 2002, 242(2):251-278.
    • (2002) Math. Z. , vol.242 , Issue.2 , pp. 251-278
    • Kozono, H.1    Ogawa, T.2    Taniuchi, Y.3
  • 21
    • 36448949849 scopus 로고    scopus 로고
    • On the global existence of smooth solution to the 2-D FENE dumbbell model
    • Lin F., Zhang P., Zhang Z. On the global existence of smooth solution to the 2-D FENE dumbbell model. Comm. Math. Phys. 2008, 277(2):531-553.
    • (2008) Comm. Math. Phys. , vol.277 , Issue.2 , pp. 531-553
    • Lin, F.1    Zhang, P.2    Zhang, Z.3
  • 22
    • 34250674362 scopus 로고    scopus 로고
    • Analytical study of certain magnetohydrodynamic-α models
    • (28 p.)
    • Linshiz J.S., Titi E.S. Analytical study of certain magnetohydrodynamic-α models. J. Math. Phys. 2007, 48(6):065504. (28 p.).
    • (2007) J. Math. Phys. , vol.48 , Issue.6 , pp. 065504
    • Linshiz, J.S.1    Titi, E.S.2
  • 23
    • 0003628399 scopus 로고    scopus 로고
    • Mathematical Topics in Fluid Mechanics, vol. 1. Incompressible Models
    • The Clarendon Press/Oxford University Press, New York
    • Lions P.-L. Mathematical Topics in Fluid Mechanics, vol. 1. Incompressible Models. Oxford Science Publications 1996, The Clarendon Press/Oxford University Press, New York.
    • (1996) Oxford Science Publications
    • Lions, P.-L.1
  • 24
    • 0034381125 scopus 로고    scopus 로고
    • Global solutions for some Oldroyd models of non-Newtonian flows
    • Lions P.-L., Masmoudi N. Global solutions for some Oldroyd models of non-Newtonian flows. Chinese Ann. Math. Ser. B 2000, 21(2):131-146.
    • (2000) Chinese Ann. Math. Ser. B , vol.21 , Issue.2 , pp. 131-146
    • Lions, P.-L.1    Masmoudi, N.2
  • 25
    • 34447298371 scopus 로고    scopus 로고
    • Global existence of weak solutions to some micro-macro models
    • Lions P.-L., Masmoudi N. Global existence of weak solutions to some micro-macro models. C. R. Math. Acad. Sci. Paris 2007, 345(1):15-20.
    • (2007) C. R. Math. Acad. Sci. Paris , vol.345 , Issue.1 , pp. 15-20
    • Lions, P.-L.1    Masmoudi, N.2
  • 26
    • 55749083845 scopus 로고    scopus 로고
    • Well-posedness for the FENE dumbbell model of polymeric flows
    • Masmoudi N. Well-posedness for the FENE dumbbell model of polymeric flows. Comm. Pure Appl. Math. 2008, 61(12):1685-1714.
    • (2008) Comm. Pure Appl. Math. , vol.61 , Issue.12 , pp. 1685-1714
    • Masmoudi, N.1
  • 27
    • 44649098150 scopus 로고    scopus 로고
    • Global well-posedness for 2D polymeric fluid models and growth estimate
    • Masmoudi N., Zhang P., Zhang Z. Global well-posedness for 2D polymeric fluid models and growth estimate. Physica D 2008, 237(10-12):1663-1675.
    • (2008) Physica D , vol.237 , Issue.10-12 , pp. 1663-1675
    • Masmoudi, N.1    Zhang, P.2    Zhang, Z.3
  • 28
    • 0004082457 scopus 로고
    • Magnetohydrodynamics
    • Kluwer Academic Publishers Group, Dordrecht, (translated from the French by A.F. Wright)
    • Moreau R. Magnetohydrodynamics. Fluid Mechanics and its Applications 1990, vol. 3. Kluwer Academic Publishers Group, Dordrecht, (translated from the French by A.F. Wright).
    • (1990) Fluid Mechanics and its Applications , vol.3
    • Moreau, R.1
  • 29
    • 0037208062 scopus 로고    scopus 로고
    • An extension of the Beale-Kato-Majda criterion for the Euler equations
    • Planchon F. An extension of the Beale-Kato-Majda criterion for the Euler equations. Comm. Math. Phys. 2003, 232(2):319-326.
    • (2003) Comm. Math. Phys. , vol.232 , Issue.2 , pp. 319-326
    • Planchon, F.1
  • 30
    • 84990557281 scopus 로고
    • Some mathematical questions related to the MHD equations
    • Sermange M., Temam R. Some mathematical questions related to the MHD equations. Comm. Pure Appl. Math. 1983, 36(5):635-664.
    • (1983) Comm. Pure Appl. Math. , vol.36 , Issue.5 , pp. 635-664
    • Sermange, M.1    Temam, R.2
  • 32
    • 38949096754 scopus 로고    scopus 로고
    • Regularity criteria for the generalized MHD equations
    • Wu J. Regularity criteria for the generalized MHD equations. Comm. Partial Differential Equations 2008, 33(1-3):285-306.
    • (2008) Comm. Partial Differential Equations , vol.33 , Issue.1-3 , pp. 285-306
    • Wu, J.1
  • 33
    • 33947375145 scopus 로고    scopus 로고
    • Regularity criteria for the generalized viscous MHD equations
    • Zhou Y. Regularity criteria for the generalized viscous MHD equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 2007, 24(3):491-505.
    • (2007) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.24 , Issue.3 , pp. 491-505
    • Zhou, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.