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In the talk we shall present some recent results obtained with F. Merle about compactness of blow up solutions of the critical nonlinear Schrödinger equation for initial data in . They are based on and are complementary to some previous work of J. Bourgain about the concentration of the solution when it approaches to the blow up time.
@incollection{JEDP_1998____A13_0, author = {Gonzalez, Luis Vega}, title = {Remarks on global existence and compactness for $L^2$ solutions in the critical nonlinear schr\"odinger equation in {2D}}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {13}, pages = {1--9}, publisher = {Universit\'e de Nantes}, year = {1998}, zbl = {01808722}, language = {en}, url = {http://geodesic.mathdoc.fr/item/JEDP_1998____A13_0/} }
TY - JOUR AU - Gonzalez, Luis Vega TI - Remarks on global existence and compactness for $L^2$ solutions in the critical nonlinear schrödinger equation in 2D JO - Journées équations aux dérivées partielles PY - 1998 SP - 1 EP - 9 PB - Université de Nantes UR - http://geodesic.mathdoc.fr/item/JEDP_1998____A13_0/ LA - en ID - JEDP_1998____A13_0 ER -
%0 Journal Article %A Gonzalez, Luis Vega %T Remarks on global existence and compactness for $L^2$ solutions in the critical nonlinear schrödinger equation in 2D %J Journées équations aux dérivées partielles %D 1998 %P 1-9 %I Université de Nantes %U http://geodesic.mathdoc.fr/item/JEDP_1998____A13_0/ %G en %F JEDP_1998____A13_0
Gonzalez, Luis Vega. Remarks on global existence and compactness for $L^2$ solutions in the critical nonlinear schrödinger equation in 2D. Journées équations aux dérivées partielles (1998), article no. 13, 9 p. http://geodesic.mathdoc.fr/item/JEDP_1998____A13_0/
[B1] Some new estimates on oscillatory integrals, Essays on Fourier Analysis in Honour of E. Stein, Princeton UP 42 (1995), 83-112 | Zbl | MR
,[B2] Refinements of Strichartz's inequality and applications to 2D-NLS with critical nonlinearity, Preprint | Zbl
,[B-L] Nonlinear scalar field equations, Arch. Rat. Mech. Anal., 82 (1983), 313-375 | Zbl | MR
,[C] An introduction to nonlinear Schrödinger equations, Textos de Metodos Matematicos 26 (Rio de Janeiro)
[C-W] Some remarks on the nonlinear Schrödinger equation in the critical case, Nonlinear semigroups, partial differential equations and attractors, Lect. Notes in Math., 1394, Spr. Ver., 1989, 18-29 | Zbl | MR
,[G] On the blowing-up of solutions to the Cauchy problem for the nonlinear Schrödinger equation, J. Math. Phys. 18 (1977), 1794-1797 | Zbl | MR
[G-V] On a class of nonlinear Schrödinger equations with nonlocal interaction, Math. Z 170, (1980), 109-136 | Zbl | MR
, ,[K] Uniqueness of positive solutions of Δu - u + up = 0 in RN, Arch. Rat. Mech. Ann. 105, (1989), 243-266 | Zbl | MR
[M1] Determination of blow-up solutions with minimal mass for non-linear Schrödinger equations with critical power, Duke Math. J., 69, (2) (1993), 427-454 | Zbl | MR
[M2] Lower bounds for the blow-up rate of solutions of the Zakharov equation in dimension two Comm. Pure and Appl. Math, Vol. XLIX, (1996), 8, 765-794 | Zbl | MR
[MV] Compactness at blow-up time for L2 solutions of the critical nonlinear Schrödinger equation. To appear in IMRN, 1998 | Zbl
,[MVV] Restriction theorems and maximal operators related to oscillatory integrals in ℝ³ to appear in Duke Math. J. | Zbl
, ,[St] Restriction of Fourier transforms to quadratic surfaces and decay of solutions to wave equations, Duke Math J., 44, (1977), 705-714 | Zbl | MR
[W] On the structure and formation of singularities of solutions to nonlinear dispersive equations Comm. P.D.E. 11, (1986), 545-565 | Zbl | MR
[ZSS] Character of the singularity and stochastic phenomena in self-focusing, Zh. Eksper. Teoret. Fiz. 14 (1971), 390-393
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