@incollection{JEDP_1997____A2_0,
author = {Thierry Cazenave},
title = {Solutions self-similaires de l'\'equation de {Schr\"odinger} non-lin\'eaire},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {2},
pages = {1--17},
publisher = {\'Ecole polytechnique},
year = {1997},
zbl = {01808662},
language = {fr},
url = {https://proceedings.centre-mersenne.org/item/JEDP_1997____A2_0/}
}
TY - JOUR AU - Thierry Cazenave TI - Solutions self-similaires de l'équation de Schrödinger non-linéaire JO - Journées équations aux dérivées partielles PY - 1997 SP - 1 EP - 17 PB - École polytechnique UR - https://proceedings.centre-mersenne.org/item/JEDP_1997____A2_0/ LA - fr ID - JEDP_1997____A2_0 ER -
Thierry Cazenave. Solutions self-similaires de l'équation de Schrödinger non-linéaire. Journées équations aux dérivées partielles (1997), article no. 2, 17 p. https://proceedings.centre-mersenne.org/item/JEDP_1997____A2_0/
[1] , A generalization of a theorem by Kato on Navier-Stokes equations, preprint. | Zbl
[2] and , Self-similar solutions for the Navier-Stokes equations in ℝ3, Comm. Partial Differential Equations 21 (1996), 179-193. | MR | Zbl
[3] and , The Cauchy problem for the critical nonlinear Schrödinger equation in Hs, Nonlinear Anal. T.M.A. 14 (1990), 807-836. | MR | Zbl
[4] and , The structure of solutions to the pseudo-conformally invariant nonlinear Schrödinger equation, Proc. Royal Soc. Edinburgh Sect. A 117 (1991), 251-273. | MR | Zbl
[5] and , Rapidly decaying solutions of the nonlinear Schrödinger equation, Comm. Math. Phys. 147 (1992), 75-100. | MR | Zbl
[6] and , Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations, Math. Z., to appear. | Zbl
[7] and , More self-similar solutions of the nonlinear Schrödinger equation, to appear. | Zbl
[8] and , Asymptotic behavior of positive solutions of a nonlinear heat equation, Houston J. Math. 13 (1987), 39-50. | Zbl
[9] and , Variational problems related to self-similar solutions of the heat equation, Nonlinear Anal. 11 (1987), 1103-1133. | MR | Zbl
[10] , and , Large time behavior of solutions of a dissipative semi-linear heat equation, Comm. Partial Differential Equations 20 (1995), 1427-1452. | MR | Zbl
[11] , On the blowing-up of solutions of the Cauchy problem for ut = Δu + uα+1, J. Fac. Sci. Univ. Tokyo 13 (1966), 109-124. | MR | Zbl
[12] , On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations, Proc. Symp. Pure Math. 18, Amer. Math. Soc., 1968, 138-161.
[13] and , On the Navier-Stokes initial value problem I, Arch. Rat. Mech. Anal. 16 (1964), 269-315. | MR | Zbl
[14] , Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system, J. Diff. Eq. 62 (1986), 186-212. | MR | Zbl
[15] and , Asymptotically self-similar blow-up of semilinear heat equations, Comm. Pure Appl. Math. 38 (1985), 297-319. | MR | Zbl
[16] and , Characterizing blow up using similarity variables, Indiana Math. J. 36 (1987), 1-40. | MR | Zbl
[17] and , Nondegeneracy of blowup for semilinear heat equations, Comm. Pure Appl. Math. 62 (1989), 845-885. | MR | Zbl
[18] and , Solutions in Lr of the Navier-Stokes initial value problem, Arch. Rat. Mech. Anal. 89 (1985), 267-281. | MR | Zbl
[19] and , Navier-Stokes flow in ℝ3 with measures as initial vorticity and Morrey spaces, Commun. Partial Differential Equations 14 (1989), 577-618. | MR | Zbl
[20] and , On a class of nonlinear Schrödinger equations I, II, J. Func. Anal. 32 (1979), 1-71. | MR | Zbl
[21] and , Non uniqueness for a semilinear initial value problem, Indiana Univ. Math. J. 31 (1982), 167-189. | MR | Zbl
[22] and , Blow-up behaviour of one-dimensional semilinear parabolic equations, Ann. Inst. Henri Poincaré, Analyse Non-Linéaire 10 (1993), 131-189. | EuDML | Numdam | MR | Zbl
[23] and , Some results on blow up for some semilinear parabolic problems, in Degenerate diffusion (Minneapolis, 1991), IMA Vol. Math. Appl. 47, Springer, New York, 1993, 105-125. | MR | Zbl
[24] and , On an elliptic equation related to the blow-up phenomenon in the non-linear Schrödinger equation, Proc. Royal Soc. Edin. Sect. A 123 (1993), 763-782. | MR | Zbl
[25] , Strong Lp solutions of the Navier-Stokes equation in ℝm, with applications to weak solutions, Math. Z. 187 (1984), 471-480. | EuDML | MR | Zbl
[26] , Nonlinear Schrödinger equations, in Schrödinger Operators, Lecture Notes in Physics 345, Springer, 1989, 218-263. | MR | Zbl
[27] and , On the nonstationary Navier-Stokes system, Rend. Sem. Mat. Univ. Padova 32 (1962), 243-260. | EuDML | Numdam | MR | Zbl
[28] , Remarks on the time behaviour of a nonlinear diffusion equation, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 4 (1987), 423-452. | EuDML | Numdam | MR | Zbl
[29] and , Self-similar solutions of the pseudo-conformally invariant nonlinear Schrödinger equation, Mich. Math. J. 41 (1992), 151-173. | MR | Zbl
[30] and , Spatial structure of the focusing singularity of the nonlinear Schrödinger equation: a geometric analysis, SIAM J. Appl. Math. 55 (1995), 1297-1323. | MR | Zbl
[31] , and , On the equation Δu + 1/2x · ∇u - u + f(u) = 0, Archive Rat. Mech. Anal. 94 (1986), 83-99. | MR | Zbl
[32] , Analyse de Littlewood Paley pour la résolution d'équations paraboliques semi-linéaires, Doctoral Thesis, University of Paris XI, January 1996.
[33] , Existence and non-existence of global solutions for a semilinear heat equation, Israel J. Math. 38 (1981), 29-40. | MR | Zbl