## Randomized final-state problem for the Zakharov system in dimension three

Spitz M (2022)
Communications in Partial Differential Equations 47(2): 346-377.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Einrichtung
Abstract / Bemerkung
We consider the final-state problem for the Zakharov system in the energy space in three space dimensions. For (u(+),v(+))is an element of H(1)xL(2) without any size restriction, symmetry assumption or additional angular regularity, we perform a physical-space randomization on u+ and an angular randomization on v(+) yielding random final states (u(+)(omega),v(+)(omega)). We obtain that for almost every omega, there is a unique solution of the Zakharov system scattering to the final state (u(+)(omega),v(+)(omega)). The key ingredient in the proof is the use of time-weighted norms and generalized Strichartz estimates which are accessible due to the randomization.
Stichworte
Almost sure scattering; final-state problem; randomized data; Zakharov; system
Erscheinungsjahr
2022
Zeitschriftentitel
Communications in Partial Differential Equations
Band
47
Ausgabe
2
Seite(n)
346 - 377
ISSN
0360-5302
eISSN
1532-4133
Page URI
https://pub.uni-bielefeld.de/record/2958887

## Zitieren

Spitz M. Randomized final-state problem for the Zakharov system in dimension three. Communications in Partial Differential Equations . 2022;47(2):346-377.
Spitz, M. (2022). Randomized final-state problem for the Zakharov system in dimension three. Communications in Partial Differential Equations , 47(2), 346-377. https://doi.org/10.1080/03605302.2021.1983595
Spitz, Martin. 2022. “Randomized final-state problem for the Zakharov system in dimension three”. Communications in Partial Differential Equations 47 (2): 346-377.
Spitz, M. (2022). Randomized final-state problem for the Zakharov system in dimension three. Communications in Partial Differential Equations 47, 346-377.
Spitz, M., 2022. Randomized final-state problem for the Zakharov system in dimension three. Communications in Partial Differential Equations , 47(2), p 346-377.
M. Spitz, “Randomized final-state problem for the Zakharov system in dimension three”, Communications in Partial Differential Equations , vol. 47, 2022, pp. 346-377.
Spitz, M.: Randomized final-state problem for the Zakharov system in dimension three. Communications in Partial Differential Equations . 47, 346-377 (2022).
Spitz, Martin. “Randomized final-state problem for the Zakharov system in dimension three”. Communications in Partial Differential Equations 47.2 (2022): 346-377.
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