The energy-critical stochastic Zakharov system

Herr S, Röckner M, Spitz M, Zhang D (Submitted) .

Preprint | Eingereicht | Englisch
 
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Abstract / Bemerkung
This work is devoted to the stochastic Zakharov system in dimension four, which is the energy-critical dimension. First, we prove local well-posedness in the energy space $H^1\times L^2$ up to the maximal existence time and a blow-up alternative. Second, we prove that for large data solutions exist globally as long as energy and wave mass are below the ground state threshold. Third, we prove a regularization by noise phenomenon: the probability of global existence and scattering goes to one if the strength of the (non-conservative) noise goes to infinity. The proof is based on the refined rescaling approach and a new functional framework, where both Fourier restriction and local smoothing norms are used as well as a (uniform) double endpoint Strichartz and local smoothing inequality for the Schr\"odinger equation with certain rough and time dependent lower order perturbations.
Erscheinungsjahr
2024
Page URI
https://pub.uni-bielefeld.de/record/2993301

Zitieren

Herr S, Röckner M, Spitz M, Zhang D. The energy-critical stochastic Zakharov system. Submitted.
Herr, S., Röckner, M., Spitz, M., & Zhang, D. (Submitted). The energy-critical stochastic Zakharov system
Herr, Sebastian, Röckner, Michael, Spitz, Martin, and Zhang, Deng. Submitted. “The energy-critical stochastic Zakharov system”.
Herr, S., Röckner, M., Spitz, M., and Zhang, D. (Submitted). The energy-critical stochastic Zakharov system.
Herr, S., et al., Submitted. The energy-critical stochastic Zakharov system.
S. Herr, et al., “The energy-critical stochastic Zakharov system”, Submitted.
Herr, S., Röckner, M., Spitz, M., Zhang, D.: The energy-critical stochastic Zakharov system. (Submitted).
Herr, Sebastian, Röckner, Michael, Spitz, Martin, and Zhang, Deng. “The energy-critical stochastic Zakharov system”. (Submitted).
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arXiv: 2410.05034

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