Dispersion and collapse of wave maps

DOI10.1088/0951-7715/13/4/323zbMath0963.35121arXivmath-ph/9912009OpenAlexW2001244357MaRDI QIDQ4508727

Tadeusz Chmaj, Zbisław Tabor, Piotr Bizoń

Publication date: 14 January 2001

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/9912009

zbMATH Keywords

self-similar solutionsCauchy problemcritical behaviour in the formation of the black holes

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Black holes (83C57) Second-order nonlinear hyperbolic equations (35L70) PDEs in connection with relativity and gravitational theory (35Q75)

Related Items (27)

Co-dimension one stable blowup for the supercritical cubic wave equation ⋮ On the existence and stability of blowup for wave maps into a negatively curved target ⋮ Construction of type II blowup solutions for the 1-corotational energy supercritical wave maps ⋮ Singularity formation in 2+1 wave maps ⋮ Harmonic and wave maps coupled with Einstein's gravitation ⋮ Threshold for blowup for equivariant wave maps in higher dimensions ⋮ Optimal blowup stability for supercritical wave maps ⋮ On stable self-similar blow up for equivariant wave maps: the linearized problem ⋮ On blowup for the supercritical quadratic wave equation ⋮ Besov Spaces and Self-Similar Solutions for the Wave-Map Equation ⋮ Threshold Behavior for Nonlinear Wave Equations ⋮ On stable self-similar blowup for equivariant wave maps ⋮ Mode stability of self-similar wave maps in higher dimensions ⋮ Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii ⋮ Numerical approaches to spacetime singularities ⋮ The Einstein-Vlasov system/kinetic theory ⋮ On blowup of co-rotational wave maps in odd space dimensions ⋮ Critical phenomena in gravitational collapse ⋮ Critical phenomena in gravitational collapse ⋮ Convergent discretization of heat and wave map flows to spheres using approximate discrete Lagrange multipliers ⋮ Global well-posedness of hedgehog solutions for the \((3+1)\) Skyrme model ⋮ SPECTRAL PROPERTIES AND LINEAR STABILITY OF SELF-SIMILAR WAVE MAPS ⋮ Decay for Skyrme wave maps ⋮ On the mode stability of a self-similar wave map ⋮ Threshold for blowup for the supercritical cubic wave equation ⋮ (In-)stability of singular equivariant solutions to the Landau–Lifshitz–Gilbert equation ⋮ Generic self-similar blowup for equivariant wave maps and Yang-Mills fields in higher dimensions

This page was built for publication: Dispersion and collapse of wave maps