Well-posedness for the Schroedinger-Improved Boussinesq System and Related Bilinear Estimates

Takafumi Akahori

Type: Article

Publication Date: 2007-01-01

Citations: 6

DOI: https://doi.org/10.1619/fesi.50.469

Abstract

We consider the Cauchy problem for the Schrödinger-improved Boussinesq system. We prove the local well-posedness below L2 and the global one in L2. The main ingredient for the local well-posedness is nearly optimal bilinear estimates related with the Schrödinger-improved Boussinesq system in the Bourgain space Xs,b.

Locations

Funkcialaj Ekvacioj - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Revisited bilinear Schrödinger estimates with applications to generalized Boussinesq equations	2020	Dan-Andrei Geba Evan Witz
+	Revisited bilinear Schr\"{o}dinger estimates with applications to generalized Boussinesq equations.	2019	Dan-Andrei Geba Evan Witz
+	Sharp local well-posedness for the "good" Boussinesq equation	2012	Nobu Kishimoto
+	Revisited bilinear Schrödinger estimates with applications to generalized Boussinesq equations	2019	Dan-Andrei Geba Evan Witz
+ PDF Chat	Sharp local well-posedness for the “good” Boussinesq equation	2012	Nobu Kishimoto
+	On the Cauchy problem for Schrödinger–improved Boussinesq equations	2019	Tohru Ozawa Kimitoshi Tsutaya
+ PDF Chat	Local well-posedness for quadratic nonlinear Schrödinger equations and the ``good'' Boussinesq equation	2010	Nobu Kishimoto Kotaro Tsugawa
+	Well-posedness of the initial-boundary value problem for the Schrödinger-Boussinesq system	2020	Boling Guo Rudong Zheng
+	On Local Well posedness of the Schrödinger-Boussinesq Systems	2022	Boling Guo Boling Guo Jie Shao Boling Guo Boling Guo
+	Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrödinger equation	2005	Ioan Bejenaru Terence Tao
+ PDF Chat	On Schrödinger-Boussinesq equations	2004	Felipe Linares A. Navas
+	Local well-posedness for the Cauchy problem of the quadratic Schrödinger equation with nonlinearity $\bar u^2$	2008	Nobu Kishimoto
+	Schrödinger-improved Boussinesq system in two space dimensions	2022	Tohru Ozawa Kenta Tomioka
+	Cauchy problem of Schrödinger-Improved Boussinesq Systems on the torus	2014	Sijia Zhong
+	Local Well-Posedness for the Derivative Nonlinear Schrödinger Equation in Besov spaces	2016	Cai Constantin Cloos
+	Local well-posedness for the quadratic Schrodinger equation in two-dimensional compact manifolds with boundary	2019	Marcelo Nogueira Mahendra Panthee
+	Local well-posedness for the quadratic Schrodinger equation in two-dimensional compact manifolds with boundary	2019	Marcelo Nogueira Mahendra Panthee
+	The nonlinear Quadratic Interactions of the Schr\"odinger type on the half-line	2021	Isnaldo Isaac Barbosa Márcio Cavalcante
+	Well-posedness of the “good” Boussinesq equation in analytic Gevrey spaces and time regularity	2019	Rafael F. Barostichi Renata O. Figueira A. Alexandrou Himonas
+	The nonlinear Quadratic Interactions of the Schrödinger type on the half-line	2021	Isnaldo Isaac Barbosa Márcio André Araújo Cavalcante

Works That Cite This (6)

Action	Title	Year	Authors
+	Cauchy problem and vanishing dispersion limit for Schrödinger-improved Boussinesq equations	2020	Jishan Fan Tohru Ozawa
+	Vanishing dispersion limit for Schrödinger-improved Boussinesq system in two space dimensions	2022	Tohru Ozawa Kenta Tomioka
+	L2$L^{2}$‐growth property for the wave equation with a higher derivative term	2024	Xiaoyan Li Ryo Ikehata
+	Well-posedness and orbital stability of traveling waves for the Schrödinger-improved Boussinesq system	2014	Amin Esfahani Ademir Pastor
+	Cauchy problem of Schrödinger-Improved Boussinesq Systems on the torus	2014	Sijia Zhong
+ PDF Chat	Schrödinger-improved Boussinesq system in two space dimensions	2022	Tohru Ozawa Kenta Tomioka

Works Cited by This (17)

Action	Title	Year	Authors
+	None	1996	Jean Bourgain J. Colliander
+	Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋	2003	J. Colliander M. Keel Gigliola Staffilani Hideo Takaoka Terence Tao
+ PDF Chat	Quadratic forms for the 1-D semilinear Schrödinger equation	1996	Carlos E. Kenig Gustavo Ponce Luis Vega
+	The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices	1993	Carlos E. Kenig Gustavo Ponce Luis Vega
+	On the Cauchy Problem for the Zakharov System	1997	J. Ginibre Yoshio Tsutsumi G. Velo
+ PDF Chat	Global solutions of the wave-Schr\"odinger system below $L^{2}$	2006	Takafumi Akahori
+	Dynamics of classical solitons (in non-integrable systems)	1978	V.G. Makhankov
+ PDF Chat	Bilinear estimates and applications to 2d NLS	2001	J. Colliander Jean-Marc Delort Carlos E. Kenig Gigliola Staffilani
+	Existence of self-similar blow-up solutions for Zakhrov equation in dimension two. Part I	1994	L. Glangetas Franck Merle
+ PDF Chat	Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems	2008	J. Colliander Justin Holmer Nikolaos Tzirakis