On the probabilistic well-posedness of the two-dimensional periodic nonlinear Schr\"odinger equation with the quadratic nonlinearity $|u|^2$

DOI10.1016/J.MATPUR.2022.12.010zbMath1507.35259arXiv2205.07797MaRDI QIDQ6399285

Ruoyuan Liu

Publication date: 16 May 2022

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Ill-posed problems for PDEs (35R25) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Fractional partial differential equations (35R11) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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