Geodesic
Nonlinear evolutionary Schr\"odinger equation in the~supercritical case
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 3, pp. 427-437

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We prove that for some initial data, solutions of the Cauchy problem for the nonlinear Schrödinger equation in the supercritical case are destroyed after a finite time, the exact value of which can be estimated from above. Lower bounds are obtained for the rate of destruction of the solution in some norms. A set of initial data is identified for which the solution of the Cauchy problem for the nonlinear Schrödinger equation in the supercritical case exists globally.
Keywords: nonlinear evolutionary Schrödinger equation, Cauchy problem, solution blow-up, blow-up rate, interpolation inequality, global solvability. 
@article{TMF_2021_209_3_a2,
     author = {Sh. M. Nasibov},
     title = {Nonlinear evolutionary {Schr\"odinger} equation in the~supercritical case},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {427--437},
     publisher = {mathdoc},
     volume = {209},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_209_3_a2/}
}
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Sh. M. Nasibov. Nonlinear evolutionary Schr\"odinger equation in the~supercritical case. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 3, pp. 427-437. http://geodesic.mathdoc.fr/item/TMF_2021_209_3_a2/