Almost sure well-posedness for the periodic 3D quintic nonlinear Schr\"odinger equation below the energy space

By Andrea R. Nahmod, Gigliola Staffilani. 2013

61 citations recorded by the source corpus.

In this paper we prove an almost sure local well-posedness result for the periodic 3D quintic nonlinear Schr\"odinger equation in the supercritical regime, that is below the critical space $H^1(\mathbb T^3)$.

Subfields: Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b13cc42d88c984748862bf97026e9c2a1b4675bd

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In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on $\mathbb{R}^d$, $d=4$ and $5$ (2014, unknown): “ollary of part (a), stating that the almost sure local existence and uniqueness still hold for more general initial data. We note that the proofs of the analogues of Theorem 1.1 for NLS on Rdand Tdin [47, 5, 6] are more intricate. Lastly, notice that Theorem 1.1 is of a local-in-time nature and henc”
On the Probabilistic Cauchy Theory of the Cubic Nonlinear Schrödinger Equation on Rd, d≥3 (2014, background): “ch that ku(t) −S(t)(φω,µ +vω +)k H d−2 2 (Rd) → 0 as t→ ∞. A similar statement holds for t→ −∞. We conclude this introduction with several remarks. Remark 1.5. In probabilistic well-posedness results [6, 7, 20, 44] for NLS on Td, random initial data are assumed to be of the following speciﬁc form: u”