On internal regularity of solutions to the initial value problem for the zakharov-kuznetsov equation

The initial value problem is considered for the Zakharov-Kuznetsov equation in two spatial dimensions, which generalizes the Korteweg-de Vries equation for description of wave propagation in dispersive media on the plane. An initial function is assumed to be irregular, namely, from the spaces L 2 or H 1. Results on gain of internal regularity for corresponding weak solutions depending on the decay rate of the initial function at infinity are established. Existence of both Sobolev and continuous derivatives of any prescribed order is proved. One of important items of the study is the investigation of the fundamental solution to the corresponding linearized equation. The obtained properties are to some extent similar to the ones of the Airy function.

Editors
-
Publisher
Springer New York LLC
Number of issue
-
Language
English
Pages
53-74
Status
Published
Department
-
Link
-
Number
-
Volume
44
Year
2013
Organizations
  • 1 Peoples' Friendship University of Russia, Miklukho-Maklai str. 6, Moscow, 117198, Russian Federation
Keywords
Initial value problem; Internal regularity; KdV-like equations; Zakharov-Kuznetsov equation
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/2140/