The Zakharov system in dimension $d>= 4$

Candy T, Herr S, Nakanishi K (Accepted)
Journal of the European Mathematical Society.

Zeitschriftenaufsatz | Angenommen | Englisch
 
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Autor*in
Candy, Timothy; Herr, SebastianUniBi ; Nakanishi, Kenji
Abstract / Bemerkung
The sharp range of Sobolev spaces is determined in which the Cauchy problem for the classical Zakharov system is well-posed, which includes existence of solutions, uniqueness, persistence of initial regularity, and real-analytic dependence on the initial data. In addition, under a condition on the data for the Schr\"odinger equation at the lowest admissible regularity, global well-posedness and scattering is proved. The results cover energy-critical and energy-supercritical dimensions $d \geqslant 4$.
Erscheinungsjahr
2020
Zeitschriftentitel
Journal of the European Mathematical Society
Page URI
https://pub.uni-bielefeld.de/record/2939554

Zitieren

Candy T, Herr S, Nakanishi K. The Zakharov system in dimension $d>= 4$. Journal of the European Mathematical Society. Accepted.
Candy, T., Herr, S., & Nakanishi, K. (Accepted). The Zakharov system in dimension $d>= 4$. Journal of the European Mathematical Society
Candy, T., Herr, S., and Nakanishi, K. (Accepted). The Zakharov system in dimension $d>= 4$. Journal of the European Mathematical Society.
Candy, T., Herr, S., & Nakanishi, K., Accepted. The Zakharov system in dimension $d>= 4$. Journal of the European Mathematical Society.
T. Candy, S. Herr, and K. Nakanishi, “The Zakharov system in dimension $d>= 4$”, Journal of the European Mathematical Society, Accepted.
Candy, T., Herr, S., Nakanishi, K.: The Zakharov system in dimension $d>= 4$. Journal of the European Mathematical Society. (Accepted).
Candy, Timothy, Herr, Sebastian, and Nakanishi, Kenji. “The Zakharov system in dimension $d>= 4$”. Journal of the European Mathematical Society (Accepted).

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arXiv: 1912.05820

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