The probabilistic scaling paradigm. (English) Zbl 07903084
Summary: In this note we further discuss the probabilistic scaling introduced by the authors in [“Invariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two”, Preprint, arXiv:1910.08492] and [Invent. Math. 228, No. 2, 539–686 (2022; Zbl 1506.35208)]. In particular we do a case study comparing the stochastic heat equation, the nonlinear wave equation and the nonlinear Schrödinger equation.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 15A69 | Multilinear algebra, tensor calculus |
| 15B52 | Random matrices (algebraic aspects) |
| 37E20 | Universality and renormalization of dynamical systems |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 60H40 | White noise theory |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35R25 | Ill-posed problems for PDEs |
Keywords:
random data theory; probabilistic scaling; NLS; NLW; stochastic heat equation; probabilistic well posedness; Gibbs measureCitations:
Zbl 1506.35208References:
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