[Un résultat dʼexplosion pour lʼéquation de Schrödinger non linéaire sans invariance de gauge dans le cas périodique]
In this Note, we prove a finite-time blowup result for the periodic nonlinear Schrödinger equation on
Dans cette Note, nous démontrons un résultat dʼexplosion en temps fini pour lʼéquation de Schrödinger non linéaire sur le tore
Accepté le :
Publié le :
Tadahiro Oh 1
@article{CRMATH_2012__350_7-8_389_0, author = {Tadahiro Oh}, title = {A blowup result for the periodic {NLS} without gauge invariance}, journal = {Comptes Rendus. Math\'ematique}, pages = {389--392}, publisher = {Elsevier}, volume = {350}, number = {7-8}, year = {2012}, doi = {10.1016/j.crma.2012.04.009}, language = {en}, }
Tadahiro Oh. A blowup result for the periodic NLS without gauge invariance. Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 389-392. doi : 10.1016/j.crma.2012.04.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.04.009/
[1] Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations I. Schrödinger equations, Geom. Funct. Anal., Volume 3 (1993) no. 2, pp. 107-156
[2] Exponential sums and nonlinear Schrödinger equations, Geom. Funct. Anal., Volume 3 (1993) no. 2, pp. 157-178
[3] Nonlinear Schrödinger equations, Park City, UT, 1995 (IAS/Park City Math. Ser.), Volume vol. 5, Amer. Math. Soc., Providence, RI (1999), pp. 3-157
[4] Semilinear Schrödinger Equations, Courant Lect. Notes Math., vol. 10, New York University, Courant Institute of Mathematical Sciences/American Mathematical Society, New York/Providence, RI, 2003 (xiv+323 pp)
[5] Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in
[6] Nonexistence of a non-trivial global weak solution for the nonlinear Schrödinger equation with a nongauge invariant power nonlinearity | arXiv
[7] Blow-up results for nonlinear parabolic equations on manifolds, Duke Math. J., Volume 97 (1999) no. 3, pp. 515-539
[8] A blow-up result for a nonlinear wave equation with damping: the critical case, C. R. Acad. Sci. Paris, Ser. I, Volume 333 (2001) no. 2, pp. 109-114
- Local Well-Posedness of the Periodic Nonlinear Schrödinger Equation with a Quadratic Nonlinearity
in Negative Sobolev Spaces, Journal of Dynamics and Differential Equations, Volume 37 (2025) no. 1, p. 509 | DOI:10.1007/s10884-023-10295-x - Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations, Mathematics of Computation, Volume 93 (2023) no. 348, p. 1569 | DOI:10.1090/mcom/3922
- Global dynamics in nonconservative nonlinear Schrödinger equations, Advances in Mathematics, Volume 398 (2022), p. 108234 | DOI:10.1016/j.aim.2022.108234
- Nonlinear smoothing for the periodic generalized nonlinear Schrödinger equation, Journal of Differential Equations, Volume 341 (2022), p. 353 | DOI:10.1016/j.jde.2022.09.017
- On global existence of L2 solutions for 1D periodic NLS with quadratic nonlinearity, Journal of Mathematical Physics, Volume 62 (2021) no. 9 | DOI:10.1063/5.0033101
- Lifespan of strong solutions to the periodic nonlinear Schrödinger equation without gauge invariance, Journal of Evolution Equations, Volume 17 (2017) no. 3, p. 1023 | DOI:10.1007/s00028-016-0364-0
- Blowup and ill-posedness results for a Dirac equation without gauge invariance, Evolution Equations and Control Theory, Volume 5 (2016) no. 2, p. 225 | DOI:10.3934/eect.2016002
- Finite time blowup of solutions to the nonlinear Schrödinger equation without gauge invariance, Journal of Mathematical Physics, Volume 57 (2016) no. 8 | DOI:10.1063/1.4960725
- Small data blow-up of L 2 or H 1-solution for the semilinear Schrödinger equation without gauge invariance, Journal of Evolution Equations, Volume 15 (2015) no. 3, p. 571 | DOI:10.1007/s00028-015-0273-7
- Some non-existence results for the semilinear Schrödinger equation without gauge invariance, Journal of Mathematical Analysis and Applications, Volume 425 (2015) no. 2, p. 758 | DOI:10.1016/j.jmaa.2015.01.003
- On Nonlinear Schrödinger Equations with Almost Periodic Initial Data, SIAM Journal on Mathematical Analysis, Volume 47 (2015) no. 2, p. 1253 | DOI:10.1137/140973384
- Small data blow-up for a system of nonlinear Schrödinger equations, Journal of Mathematical Analysis and Applications, Volume 399 (2013) no. 1, p. 147 | DOI:10.1016/j.jmaa.2012.10.003
Cité par 12 documents. Sources : Crossref
Commentaires - Politique
Vous devez vous connecter pour continuer.
S'authentifier