no. 4
Global solutions to vortex density equations arising from sup-conductivity
Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 4, pp. 441-458 
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     author = {Masmoudi, Nader and Zhang, Ping},
     title = {Global solutions to vortex density equations arising from sup-conductivity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {441--458},
     year = {2005},
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Masmoudi, Nader; Zhang, Ping. Global solutions to vortex density equations arising from sup-conductivity. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 4, pp. 441-458. doi: 10.1016/j.anihpc.2004.07.002

[1] Chapman J.S., Rubinstein J.K., Schatzman M., A mean-field model of superconducting vortices, Eur. J. Appl. Math. 7 (1996) 97-111. | Zbl | MR

[2] Chemin J.Y., Persistance de structures géométriques dans les fluides incompressibles bidimensionnels, Ann. Sci. École Norm. Sup. 26 (1993) 517-542. | Zbl | MR | Numdam

[3] Diperna R.J., Lions P.L., Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989) 511-547. | Zbl | MR

[4] Diperna R.J., Lions P.L., On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. of Math. (2) 130 (1989) 321-366. | Zbl | MR

[5] Diperna R.J., Majda A., Oscillations and concentrations in weak solutions of the incompressible fluid equations, Comm. Math. Phys. 108 (1987) 667-689. | Zbl | MR

[6] Du Q., Zhang P., Existence of weak solutions to some vortex density models, SIAM J. Math. Anal. 34 (2003) 1279-1299. | Zbl | MR

[7] Delort J.M., Existence de nappes de tourbillon en dimension deux, J. Amer. Math. Soc. 4 (1991) 553-586. | Zbl | MR

[8] Elliott C.M., Schätzle R., Stoth B.E.E., Viscosity solutions of a degenerate parabolic-elliptic system arising in the mean-field theory of superconductivity, Arch. Rational Mech. Anal. 145 (1998) 99-127. | Zbl | MR

[9] Evans L.C., Weak Convergence Methods for Nonlinear Partial Differential Equations, CBMS, vol. 74, Amer. Math. Soc., Providence, RI, 1990. | Zbl | MR

[10] Jerrard R.L., Soner H.M., Dynamics of Ginzburg-Landau vortices, Arch. Rational Mech. Anal. 142 (1998) 99-125. | Zbl | MR

[11] Joly J.L., Métivier G., Rauch J., Focusing at a point and absorption of nonlinear oscillations, Trans. Amer. Math. Soc. 347 (1995) 3921-3970. | Zbl | MR

[12] Lin F., Some dynamical properties of Ginzburg-Landau vortices, Comm. Pure Appl. Math. 51 (1998) 323-359. | Zbl | MR

[13] Lin F., Zhang P., On the hydrodynamic limit of Ginzburg-Landau vortices, Discrete Contin. Dynam. Systems 6 (2000) 121-142. | Zbl | MR

[14] Lions P.L., Mathematical Topics in Fluid Mechanics, vol. 2, Compressible Models, Lecture Series in Mathematics and its Applications, vol. 6, Clarendon Press, Oxford, 1998. | Zbl | MR

[15] Lions P.-L., Masmoudi N., Global solutions for some Oldroyd models of non-Newtonian flows, Chinese Ann. Math. Ser. B 21 (2000) 131-146. | Zbl | MR

[16] Schonbek M., Convergence of solutions to nonlinear dispersive equations, Comm. Partial Differential Equations 7 (1982) 959-1000. | Zbl | MR

[17] Tartar L., Compensated compactness and applications to partial differential equations, in: Knops R.J. (Ed.), Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Research Notes in Math., vol. 39, Pitman, 1979. | Zbl | MR

[18] Vecchi I., Wu S., On L 1 -vorticity for 2-D incompressible flow, Manuscripta Math. 78 (1993) 403-412. | Zbl | MR

[19] Weinan E., Dynamics of vortex liquids in Ginsburg-Landau theories with application to superconductivity, Phys. Rev. B 50 (1994) 1126-1135. | Zbl

[20] Young L.C., Lectures on the Calculus of Variations and Optimal Control Theory, Saunders, Philadelphia, 1969. | Zbl | MR

[21] Yudovich V.I., Nonstationary flow of an ideal incompressible liquid, Zh. Vych. Math. 3 (1963) 1032-1066, (in Russian). English translation, USSR Comput. Math. Phys. 3 (1963) 1407-1456. | Zbl

[22] Zhang P., Zheng Y., Existence and uniqueness of solutions to an asymptotic equation of a variational wave equation with general data, Arch. Rational Mech. Anal. 155 (2000) 49-83. | Zbl | MR

[23] Zhang P., Zheng Y., Rarefactive solutions to a nonlinear variational wave equation, Comm. Partial Differential Equations 26 (2001) 381-420. | Zbl | MR

[24] P. Zhang, Y. Zheng, Weak solutions to a nonlinear variational wave equation with general data, Ann. Inst. H. Poincaré Anal. Non Linéaire (2005), in press. | Zbl | MR | Numdam

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