On the Existence of the Solution of the Time Dependent Ginzburg-Landau Equations in $R^3$

MR1795973 Takahiro AKIYAMA, Hironori KASAI and Masayoshi TSUTSUMI Takahiro AKIYAMA, Hironori KASAI and Masayoshi TSUTSUMI On the Existence of the Solution of the Time Dependent Ginzburg-Landau Equations in $R^3$ Funkcialaj Ekvacioj. Serio Internacia 43 2000 255--270 http://fe.math.kobe-u.ac.jp/FE/FullPapers/vol43/fe43-2-4.pdf http://www.ams.org/mathscinet-getitem?mr=MR1795973 43-255 2000 On the Existence of the Solution of the Time Dependent Ginzburg-Landau Equations in $R^3$ Takahiro AKIYAMA, Hironori KASAI and Masayoshi TSUTSUMI Takahiro AKIYAMA, Hironori KASAI and Masayoshi TSUTSUMI 1 Giga, Y., Regularity criteria for weak solutions of the Navier-Stokes system, Proceedings. Amer. Math. Soc. Summer Inst. (1983) in press MR0843578

2 Gor'kov, L. P.; Eliashberg, G. M. Generalization of Ginzburg-Landau equations for non-stationary problems in the case of alloys with paramagnetic impurities Soviet Phys. J.E.T.P. 27 1968 328-334

3 Kato, T. Strong $L^p$-solutions of the Navier-Stokes Equation in $R^n$ with Applications to Weak solutions Math. Z. 187 1984 481-490 MR0760047

4 Pazy, A. Semigroup of Linear Operators and Applications to Partial Differential Equations (2nd edition) Springer Verlag MR0710486

5 Schmid, A. A time dependent Ginzburg-Landau equation and its application to the problem of resistivity in the mixed state Phys. Kondens. Materie 5 1966 302-317

6 Tang, Qi On Evolution System of Ginzburg-Landau Equations with Fixed Total Magnetic Flux Commun. in Partial Differential Equations 20 1995 1-36 MR1312698

7 Tang, Qi; Wang, S. Time dependent Ginzburg-Landau equations of superconductivity Physica D 88 1995 139-166 MR1360881

8 Tsutsumi, M.; Kasai, H. The Time Dependent Ginzburg-Landau Maxwell Equations Nonlinear Analysis 37 1999 187-216 MR1689748