A codimension-two stable manifold of near soliton equivariant wave maps

Ioan Bejenaru, Joachim Krieger, Daniel Tataru

Type: Article

Publication Date: 2013-08-21

Citations: 12

DOI: https://doi.org/10.2140/apde.2013.6.829

Abstract

We consider finite energy equivariant solutions for the wave map problem from R 2+1 to S 2 which are close to the soliton family.We prove asymptotic orbital stability for a codimension two class of initial data which is small with respect to a stronger topology than the energy.

Locations

Analysis & PDE - View - PDF
eScholarship (California Digital Library) - View - PDF
arXiv (Cornell University) - View - PDF
Infoscience (Ecole Polytechnique Fédérale de Lausanne) - View - PDF
Project Euclid (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	A codimension two stable manifold of near soliton equivariant wave maps	2011	Ioan Bejenaru Joachim Krieger Daniel Tataru
+	A codimension two stable manifold of near soliton equivariant wave maps	2011	Ioan Bejenaru Joachim Krieger Daniel Tataru
+	Infinite Time Blow-Up Solutions to the Energy Critical Wave Maps Equation	2023	Mohandas Pillai
+	Asymptotic stability of small energy harmonic maps under the wave map on 2D hyperbolic space	2017	Ze Li Xiao Ma Lifeng Zhao
+ PDF Chat	Threshold for blowup for equivariant wave maps in higher dimensions	2017	Paweł Biernat Piotr Bizoń Maciej Maliborski
+ PDF Chat	Characterization of large energy solutions of the equivariant wave map problem: I	2015	Raphaël Côte Carlos E. Kenig Andrew Lawrie Wilhelm Schlag
+	On stable self-similar blow up for equivariant wave maps	2010	Roland Donninger
+	On stable self-similar blow up for equivariant wave maps	2010	Roland Donninger
+ PDF Chat	On stable self-similar blowup for equivariant wave maps	2011	Roland Donninger
+	Global, Non-scattering solutions to the energy critical wave maps equation	2020	Mohandas Pillai
+	On the soliton resolution conjecture for wave maps	2016	Roland Grinis
+	Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions	2014	Ioan Bejenaru Daniel Tataru
+ PDF Chat	On the existence and stability of blowup for wave maps into a negatively curved target	2018	Roland Donninger Irfan Glogić
+ PDF Chat	Characterization of large energy solutions of the equivariant wave map problem: II	2015	Raphaël Côte Carlos E. Kenig Andrew Lawrie Wilhelm Schlag
+	Characterization of large energy solutions of the equivariant wave map problem: II	2012	Raphaël Côte Carlos E. Kenig Andrew Lawrie Wilhelm Schlag
+	Infinite time blow-up solutions to the energy critical wave maps equation	2019	Mohandas Pillai
+ PDF Chat	On Stable Self-Similar Blow up for Equivariant Wave Maps: The Linearized Problem	2011	Roland Donninger Birgit Schörkhuber P. C. Aichelburg
+ PDF Chat	Global, Non-Scattering Solutions to the Energy Critical Wave Maps Equation	2023	Mohandas Pillai
+	A continuum of infinite time blow-up solutions to the energy critical wave maps equation	2019	Mohandas Pillai
+ PDF Chat	Sharp Universal Rate for Stable Blow-Up of Corotational Wave Maps	2023	Kihyun Kim

Works That Cite This (11)

Action	Title	Year	Authors
+	Asymptotic stability of large energy harmonic maps under the wave map from 2D hyperbolic spaces to 2D hyperbolic spaces	2020	Ze Li
+	Infinite Time Blow-Up Solutions to the Energy Critical Wave Maps Equation	2023	Mohandas Pillai
+ PDF Chat	On the stability of blowup solutions for the critical corotational wave-map problem	2020	Joachim Krieger Shuang Miao
+ PDF Chat	Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space	2016	Roland Donninger Joachim Krieger Jérémie Szeftel Willie Wai-Yeung Wong
+ PDF Chat	Global, Non-Scattering Solutions to the Energy Critical Wave Maps Equation	2023	Mohandas Pillai
+ PDF Chat	Characterization of large energy solutions of the equivariant wave map problem: II	2015	Raphaël Côte Carlos E. Kenig Andrew Lawrie Wilhelm Schlag
+ PDF Chat	Global, non-scattering solutions to the energy critical Yang–Mills problem	2021	Mohandas Pillai
+ PDF Chat	The Cauchy Problem for Wave Maps on Hyperbolic Space in Dimensions $d\geq 4$	2016	Andrew Lawrie Sung‐Jin Oh Sohrab Shahshahani
+ PDF Chat	Construction of Blow-Up Manifolds to the Equivariant Self-dual Chern–Simons–Schrödinger Equation	2023	Kihyun Kim Soonsik Kwon
+	Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case	2017	Ze Li Xiao Ma Lifeng Zhao

Works Cited by This (10)

Action	Title	Year	Authors
+	Near soliton evolution for equivariant Schroedinger Maps in two spatial dimensions	2010	Ioan Bejenaru Daniel Tataru
+ PDF Chat	On the formation of singularities in the critical<i>O</i>(3)<i>σ</i>-model	2010	Igor Rodnianski Jacob Sterbenz
+ PDF Chat	On the focusing critical semi-linear wave equation	2007	John N. Krieger Wilhelm Schlag
+ PDF Chat	Asymptotic Stability, Concentration, and Oscillation in Harmonic Map Heat-Flow, Landau-Lifshitz, and Schrödinger Maps on $${\mathbb R^2}$$	2010	Stephen J. Gustafson Kenji Nakanishi Tai‐Peng Tsai
+ PDF Chat	Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems	2012	Pierre Raphaël Igor Rodnianski
+	Equivariant wave maps in two space dimensions	2003	Michaël Struwe
+ PDF Chat	Formation of singularities for equivariant (2+1)-dimensional wave maps into the 2-sphere	2001	Piotr Bizoń Tadeusz Chmaj Zbisław Tabor
+ PDF Chat	Asymptotic stability of harmonic maps under the Schrödinger flow	2008	Stephen J. Gustafson Kyungkeun Kang Tai‐Peng Tsai
+	Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions	2014	Ioan Bejenaru Daniel Tataru
+ PDF Chat	Renormalization and blow up for charge one equivariant critical wave maps	2007	John Krieger Wilhelm Schlag Daniel Tataru