Subcritical well-posedness results for the Zakharov–Kuznetsov equation in dimension three and higher

Sebastian Herr, S. Kinoshita

Type: Article

Publication Date: 2022-11-28

Citations: 11

DOI: https://doi.org/10.5802/aif.3547

Abstract

The Zakharov–Kuznetsov equation in space dimension d≥3 is considered. It is proved that the Cauchy problem is locally well-posed in H s (ℝ d ) in the full subcritical range s>(d-4)/2, which is optimal up to the endpoint. As a corollary, global well-posedness in L 2 (ℝ 3 ) and, under a smallness condition, in H 1 (ℝ 4 ), follow.

Locations

arXiv (Cornell University) - View - PDF
Annales de l’institut Fourier - View - PDF

Similar Works

Action	Title	Year	Authors
+	Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher	2020	Sebastian Herr S. Kinoshita
+	The Zakharov system in dimension $d \geqslant 4$	2019	Timothy Candy Sebastian Herr Kenji Nakanishi
+	Well-Posedness for the Two-Dimensional Modified Zakharov–Kuznetsov Equation	2009	Felipe Linares Ademir Pastor
+	The Zakharov system in dimension $ d \geq 4$	2022	Timothy Candy Sebastian Herr Kenji Nakanishi
+ PDF Chat	Global well-posedness for the 3D Zakharov-Kuznetsov equation in energy space $H^1$	2016	Qiaoxin Li Yueling Jia Zhaohi Huo
+	Well-posedness for the Cauchy problem of the modified Zakharov-Kuznetsov equation	2019	S. Kinoshita
+	Local Well-Posedness for the Zakharov System in Dimension $d\leqslant 3$	2021	Akansha Sanwal
+	Well-posedness results for the 3D Zakharov-Kuznetsov equation	2011	Francis Ribaud Stéphane Vento
+	The Cauchy problem for the 3D Zakharov-Kuznetsov equation	2009	Felipe Linares Jean‐Claude Saut
+ PDF Chat	Well-posedness and scattering for the Zakharov system in four dimensions	2015	Ioan Bejenaru Zihua Guo Sebastian Herr Kenji Nakanishi
+ PDF Chat	Local well-posedness for the Zakharov-Kuznetsov equation on the background of a bounded function	2024	José M. Palacios
+	Well-Posedness Results for the Three-Dimensional Zakharov--Kuznetsov Equation	2012	Francis Ribaud Stéphane Vento
+ PDF Chat	Global well-posedness for the Cauchy problem of the Zakharov–Kuznetsov equation in 2D	2020	S. Kinoshita
+	Local well-posedness for the Zakharov system in dimension $d=2, 3$	2021	Zijun Chen Shengkun Wu
+	Local Existence of Strong Solutions to the 3D Zakharov-Kuznestov Equation in a Bounded Domain	2013	Chuntian Wang
+	Local ill-posedness of the 1D Zakharov system	2006	Justin Holmer
+	A Remark on the modified Zakharov-Kuznetsov equation in three space dimensions	2013	Axel Grünrock
+	A note on the 2D generalized Zakharov-Kuznetsov equation: local, global, and scattering results	2011	Luiz Gustavo Farah Felipe Linares Ademir Pastor
+	A note on the 2D generalized Zakharov-Kuznetsov equation: local, global, and scattering results	2011	Luiz Gustavo Farah Felipe Linares Ademir Pastor
+	Local well-posedness for the Zakharov-Kuznetsov equation on the background of a bounded function	2022	José Manuel Palacios

Works That Cite This (11)

Action	Title	Year	Authors
+ PDF Chat	On the propagation of regularity for solutions of the Zakharov–Kuznetsov equation	2023	Argenis J. Mendez
+ PDF Chat	Existence of solutions for the surface electromigration equation	2021	Felipe Linares Ademir Pastor M. Scialom
+ PDF Chat	Numerical study of soliton stability, resolution and interactions in the 3D Zakharov–Kuznetsov equation	2021	Christian Klein Svetlana Roudenko Nikola Stoilov
+ PDF Chat	On decay properties for solutions of the Zakharov–Kuznetsov equation	2024	A. J. Mendez Oscar Riaño
+ PDF Chat	On the nonlinear Brascamp–Lieb inequality	2020	Jonathan Bennett Neal Bez Stefan Buschenhenke Michael Cowling Taryn C. Flock
+	Local well-posedness and spatial analyticity for the generalized Zakharov–Kuznetsov equation	2023	H S Qian Minjie Shan
+ PDF Chat	Asymptotic stability of a finite sum of solitary waves for the Zakharov–Kuznetsov equation	2024	Didier Pilod Frédéric Valet
+	Pointwise convergence and nonlinear smoothing of the generalized Zakharov–Kuznetsov equation	2024	Wei Yan Weimin Wang Xiangqian Yan
+	Review on long time asymptotics of large data in some nonintegrable dispersive models	2023	Claudio Muñoz
+	Dynamics of the Collision of Two Nearly Equal Solitary Waves for the Zakharov–Kuznetsov Equation	2024	Didier Pilod Frédéric Valet

Works Cited by This (24)

Action	Title	Year	Authors
+	Well-posedness Results for the Modified Zakharov-Kuznetsov Equation	2003	H. A. Biagioni Felipe Linares
+ PDF Chat	The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation	2013	David Lannes Felipe Linares Jean–Claude Saut
+	On the Cauchy Problem for the Zakharov System	1997	J. Ginibre Yoshio Tsutsumi G. Velo
+ PDF Chat	A non-linear generalisation of the Loomis-Whitney inequality andapplications	2005	Jonathan Bennett Anthony Carbery James Wright
+	The Cauchy problem for the 3D Zakharov-Kuznetsov equation	2009	Felipe Linares Jean‐Claude Saut
+	Well-Posedness for the Two-Dimensional Modified Zakharov–Kuznetsov Equation	2009	Felipe Linares Ademir Pastor
+ PDF Chat	A note on the 2D generalized Zakharov–Kuznetsov equation: Local, global, and scattering results	2012	Luiz Gustavo Farah Felipe Linares Ademir Pastor
+	Well-Posedness Results for the Three-Dimensional Zakharov--Kuznetsov Equation	2012	Francis Ribaud Stéphane Vento
+ PDF Chat	Convolutions of singular measures and applications to the Zakharov system	2011	Ioan Bejenaru Sebastian Herr
+ PDF Chat	Bilinear Strichartz estimates for the Zakharov–Kuznetsov equation and applications	2014	Didier Pilod Luc Molinet