Existence of the self-similar solutions in the heat flow of harmonic maps

DOI10.1007/BF02876563zbMath0926.35021MaRDI QIDQ1283086

Huijun Fan

Publication date: 15 November 1999

Published in: Science in China. Series A (Search for Journal in Brave)

zbMATH Keywords

Beltrami-Laplace operatorsingularity of the first kind

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (18)

Liouville property for a class of quasi-harmonic sphere ⋮ Construction of a spectrally stable self-similar blowup solution to the supercritical corotational harmonic map heat flow ⋮ Non existence of quasi-harmonic spheres ⋮ Recent results for the Landau-Lifshitz equation ⋮ On the stability of type II blowup for the 1-corotational energy-supercritical harmonic heat flow ⋮ Stable self-similar blowup in the supercritical heat flow of harmonic maps ⋮ Transition of blow-up mechanisms ink-equivariant harmonic map heat flow ⋮ Selfsimilar expanders of the harmonic map flow ⋮ Nonlinear stability of homothetically shrinking Yang-Mills solitons in the equivariant case ⋮ Local regularity for the harmonic map and Yang-Mills heat flows ⋮ \(\mathcal{F}\)-stability of self-similar solutions to harmonic map heat flow ⋮ Self-similar shrinkers of the one-dimensional Landau-Lifshitz-Gilbert equation ⋮ Elliptic equations strongly degenerate at a point ⋮ Liouville theorems for quasi-harmonic functions ⋮ Type II blow-up mechanisms in a semilinear heat equation with critical Joseph-Lundgren exponent ⋮ Self-similar solutions of Schrödinger flows ⋮ Generic self-similar blowup for equivariant wave maps and Yang-Mills fields in higher dimensions ⋮ Ginzburg-Landau vortices with pinning functions and self-similar solutions in harmonic maps

Cites Work

• Estimate of singular set of the evolution problem for harmonic maps
• On the evolution of harmonic mappings of Riemannian surfaces
• Existence and partial regularity results for the heat flow for harmonic maps
• Finite-time blow-up of the heat flow of harmonic maps from surfaces
• Harmonic Mappings of Riemannian Manifolds
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