Rough solutions for the wave maps equation
From MaRDI portal
Publication:4676364
DOI10.1353/ajm.2005.0014zbMath1330.58021OpenAlexW2146267354WikidataQ60019393 ScholiaQ60019393MaRDI QIDQ4676364
Publication date: 3 May 2005
Published in: American Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1353/ajm.2005.0014
Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for second-order hyperbolic equations (35L15) Hyperbolic equations on manifolds (58J45)
Related Items (59)
Local well-posedness for quasi-linear problems: A primer ⋮ On the Soliton Resolution for Equivariant Wave Maps to the Sphere ⋮ Global existence and lifespan of smooth solutions of biwave maps ⋮ Global existence and uniqueness of Schrödinger maps in dimensions \(d\geq 4\) ⋮ Global regularity for the Maxwell-Klein-Gordon equation with small critical Sobolev norm in high dimensions ⋮ Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation ⋮ Concentration compactness for the critical Maxwell-Klein-Gordon equation ⋮ Local well-posedness of the \((4 + 1)\)-dimensional Maxwell-Klein-Gordon equation at energy regularity ⋮ Concentration compactness for critical radial wave maps ⋮ Global well-posedness for the three dimensional simplified inertial Ericksen-Leslie systems near equilibrium ⋮ On the stability of blowup solutions for the critical corotational wave-map problem ⋮ Optimal blowup stability for supercritical wave maps ⋮ Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: energy critical case ⋮ Asymptotic stability of large energy harmonic maps under the wave map from 2D hyperbolic spaces to 2D hyperbolic spaces ⋮ Some properties of biwave maps ⋮ The wave maps equation and Brownian paths ⋮ Sharp universal rate for stable blow-up of corotational wave maps ⋮ On stable self-similar blow up for equivariant wave maps: the linearized problem ⋮ Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces ⋮ On the stability of certain spin models in \(2+1\) dimensions ⋮ The time-like minimal surface equation in Minkowski space: low regularity solutions ⋮ Continuous dependence of Cauchy problem for nonlinear Schrödinger equation in \(H^s\) ⋮ Global Schrödinger maps in dimensions \(d\geq 2\): small data in the critical Sobolev spaces ⋮ Global well-posedness for half-wave maps with \(S^2\) and \(\mathbb{H}^2\) targets for small smooth initial data ⋮ Transversal wave maps and transversal exponential wave maps ⋮ Quasilinear Schrödinger equations. I: Small data and quadratic interactions ⋮ Quadratic nonlinear derivative Schrödinger equations - Part 2 ⋮ Besov Spaces and Self-Similar Solutions for the Wave-Map Equation ⋮ The threshold theorem for the $(4+1)$-dimensional Yang–Mills equation: An overview of the proof ⋮ On the division problem for the wave maps equation ⋮ Wave maps on \((1+2)\)-dimensional curved spacetimes ⋮ The threshold conjecture for the energy critical hyperbolic Yang-Mills equation ⋮ Low-regularity Schrödinger maps. II: Global well-posedness in dimensions \(d \geq 3\) ⋮ On stable self-similar blowup for equivariant wave maps ⋮ Renormalization and blow up for charge one equivariant critical wave maps ⋮ Quantization of time-like energy for wave maps into spheres ⋮ The Cauchy problem for wave maps on a curved background ⋮ On blowup of co-rotational wave maps in odd space dimensions ⋮ Unnamed Item ⋮ Global well-posedness for the massive Maxwell-Klein-Gordon equation with small critical Sobolev data ⋮ Energy dispersed large data wave maps in \(2+1\) dimensions ⋮ Regularity of wave-maps in dimension \(2+1\) ⋮ On collapse of wave maps ⋮ On the formation of singularities in the critical \(O(3)\) \(\sigma \)-model ⋮ Renormalization and blow-up for wave maps from 𝑆²×ℝ to 𝕊² ⋮ MultiSymplectic Discretization of Wave Map Equations ⋮ Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: high dimensions ⋮ The wave maps equation ⋮ Almost optimal local well-posedness for the (3+1)-dimensional Maxwell–Klein–Gordon equations ⋮ Quasilinear Schrödinger equations. III: Large data and short time. ⋮ Biwave maps into manifolds ⋮ LONG TIME SOLUTIONS FOR WAVE MAPS WITH LARGE DATA ⋮ Global regularity of wave maps from \(\mathbb{R}^{2+1}\) to \(H^{2}\). Small energy ⋮ The Concentration-Compactness Rigidity Method for Critical Dispersive and Wave Equations ⋮ Global well-posedness for the Maxwell-Klein-Gordon equation in \(4+1\) dimensions: small energy ⋮ Absence of self-similar blow-up and local well-posedness for the constant mean-curvature wave equation ⋮ Non-uniqueness of weak solutions to the wave map problem ⋮ Optimal polynomial blow up range for critical wave maps ⋮ Stability of stationary wave maps from a curved background to a sphere
This page was built for publication: Rough solutions for the wave maps equation