Non-uniqueness of weak solutions to the wave map problem

Klaus Widmayer

Type: Article

Publication Date: 2014-02-21

Citations: 5

DOI: https://doi.org/10.1016/j.anihpc.2014.02.001

View Publication

Locations

Annales de l Institut Henri Poincaré C Analyse Non Linéaire - View
arXiv (Cornell University) - View - PDF
French digital mathematics library (Numdam) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class	2008	Terence Tao
+	Energy bounds for a fourth-order equation in low dimensions related to wave maps	2022	Tobias Schmid
+	A new $p$-harmonic map flow with Struwe monotonicity	2023	Erik Hupp Michał Miśkiewicz
+ PDF Chat	On Uniqueness for the Harmonic Map Heat Flow in Supercritical Dimensions	2017	Pierre Germain Tej‐Eddine Ghoul Hideyuki Miura
+	Energy bounds for biharmonic wave maps in low dimensions	2018	Tobias Schmid
+	Wave Maps and Ill-posedness of their Cauchy Problem	2006	Piero DʼAncona Vladimir Georgiev
+ PDF Chat	Non-uniqueness of mild solutions to supercritical heat equations	2025	Irfan Glogić Martina Hofmanová Theresa Lange Eliseo Luongo
+	On uniqueness for the Harmonic Map Heat Flow in supercritical dimensions	2016	Pierre Germain Tej‐Eddine Ghoul Hideyuki Miura
+ PDF Chat	Low regularity solutions for the wave map equation into the 2-D sphere	2004	Piero DʼAncona Vladimir Georgiev
+ PDF Chat	An improved uniqueness result for the harmonic map flow in two dimensions	2008	Melanie Rupflin
+ PDF Chat	Heat flow and boundary value problem for harmonic maps	1989	Chang Kungching
+	The wave map problem. Small data critical regularity	2006	Igor Rodnianski
+	Almost sure existence of global solutions for supercritical semilinear wave equations	2020	Mickaël Latocca
+ PDF Chat	Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions	2013	Aynur Bulut Magdalena Czubak Dong Li Nataša Pavlović Xiaoyi Zhang
+	Point Singularities and Nonuniqueness for the Heat Flow for Harmonic Maps	2003	Michiel Bertsch Roberta Dal Passo Adriano Pisante
+ 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	Global Well-Posedness and Soliton Resolution for the Half-Wave Maps Equation with Rational Data	2024	Patrick Gérard Enno Lenzmann
+	Uniqueness of harmonic maps with small energy	1998	Michaël Struwe
+	Large global solutions for energy supercritical nonlinear wave equations on \R^{3+1}	2014	Joachim Krieger Wilhelm Schlag
+ PDF Chat	Large global solutions for energy supercritical nonlinear wave equations on ℝ3+1	2017	Joachim Krieger Wilhelm Schlag

Works That Cite This (5)

Action	Title	Year	Authors
+ PDF Chat	Hyperboloidal Similarity Coordinates and a Globally Stable Blowup Profile for Supercritical Wave Maps	2019	Paweł Biernat Roland Donninger Birgit Schörkhuber
+	On uniqueness for the Harmonic Map Heat Flow in supercritical dimensions	2016	Pierre Germain Tej‐Eddine Ghoul Hideyuki Miura
+ PDF Chat	A posteriori error estimates for wave maps into spheres	2023	Jan Giesselmann Elena Mäder-Baumdicker David Jakob Stonner
+	Hyperboloidal similarity coordinates and a globally stable blowup profile for supercritical wave maps	2017	Paweł Biernat Roland Donninger Birgit Schörkhuber
+ PDF Chat	On Uniqueness for the Harmonic Map Heat Flow in Supercritical Dimensions	2017	Pierre Germain Tej‐Eddine Ghoul Hideyuki Miura

Works Cited by This (18)

Action	Title	Year	Authors
+ PDF Chat	Nonuniqueness for the heat flow of harmonic maps	1990	Jean‐Michel Coron
+ PDF Chat	On stable self-similar blowup for equivariant wave maps	2011	Roland Donninger
+	Weak solutions and development of singularities of the SU(2) σ‐model	1988	Jalal Shatah
+	Uniqueness for critical nonlinear wave equations and wave maps via the energy inequality	1999	Michaël Struwe
+	Besov Spaces and Self-Similar Solutions for the Wave-Map Equation	2008	Pierre Germain
+	Global weak solutions of the wave map system to compact homogeneous spaces	1996	André Pimenta Freire
+	Smoothing estimates for null forms and applications	1995	Sergiù Klainerman Matei Machedon
+ PDF Chat	Formation of singularities for equivariant (2+1)-dimensional wave maps into the 2-sphere	2001	Piotr Bizoń Tadeusz Chmaj Zbisław Tabor
+	Remark on the optimal regularity for equations of wave maps type	1997	Sergiù Klainerman Sigmund Selberg
+ PDF Chat	Global Regularity of Wave Maps¶II. Small Energy in Two Dimensions	2001	Terence Tao