Publicação
On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity
| Resumo: | We study the nonlinear Schrödinger equation [vg. equation] … After showing that the linear Schrödinger group is well-defined in this space, we prove local well-posedness in the whole range of parameters s and p. The precise properties of the solution depend on the relation between the power of the nonlinearity and the integrability p. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method properties of the solution depend on the relation between the power of the nonlinearity and the integrability p. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method. |
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| Autores principais: | Barros, Vanessa |
| Outros Autores: | Correia, Simão; Oliveira, Filipe |
| Assunto: | Nonlinear Schrödinger Equation Local Well-Posedness |
| Ano: | 2022 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| Resumo: | We study the nonlinear Schrödinger equation [vg. equation] … After showing that the linear Schrödinger group is well-defined in this space, we prove local well-posedness in the whole range of parameters s and p. The precise properties of the solution depend on the relation between the power of the nonlinearity and the integrability p. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method properties of the solution depend on the relation between the power of the nonlinearity and the integrability p. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method. |
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