Infinite-time blowing-up solutions to small perturbations of the Yamabe flow

DOI10.1016/j.aim.2024.109611arXiv2106.09220OpenAlexW4393024716MaRDI QIDQ6126740

Seunghyeok Kim, Monica Musso

Publication date: 10 April 2024

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.09220

zbMATH Keywords

fast diffusion equationbubbledegenerate parabolic equationcompact Riemannian manifoldYamabe-type flow

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Blow-up in context of PDEs (35B44) Quasilinear parabolic equations (35K59) Ricci flows (53E20)

Cites Work

• Unnamed Item
• Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5
• Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem
• Nonscattering solutions and blowup at infinity for the critical wave equation
• Behaviour near extinction for the fast diffusion equation on bounded domains
• Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems
• Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
• Convergence of the Yamabe flow for arbitrary initial energy
• On the formation of singularities in the critical \(O(3)\) \(\sigma \)-model
• A compactness theorem for the Yamabe problem
• Blow-up phenomena for the Yamabe equation. II
• Slow blow-up solutions for the \(H^1(\mathbb R^3)\) critical focusing semilinear wave equation
• Conformal deformation of a Riemannian metric to constant scalar curvature
• A note on the Sobolev inequality
• Finite-time blow-up of the heat flow of harmonic maps from surfaces
• Global existence and convergence of Yamabe flow
• Type II ancient compact solutions to the Yamabe flow
• Positive clusters for smooth perturbations of a critical elliptic equation in dimensions four and five
• Repulsion and quantization in almost-harmonic maps, and asymptotic of the harmonic map flow
• Type II blow-up for the four dimensional energy critical semi linear heat equation
• Smooth type II blow-up solutions to the four-dimensional energy-critical wave equation
• Towers of bubbles for Yamabe-type equations and for the Brézis-Nirenberg problem in dimensions \(n \geq 7\)
• Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5
• Geometry driven type II higher dimensional blow-up for the critical heat equation
• Singularity formation for the two-dimensional harmonic map flow into \(S^2\)
• Infinite-time blow-up for the 3-dimensional energy-critical heat equation
• Green's function and infinite-time bubbling in the critical nonlinear heat equation
• A higher speed type II blowup for the five dimensional energy critical heat equation
• Slowly converging Yamabe flows
• The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
• Clustered solutions for supercritical elliptic equations on Riemannian manifolds
• Classification of the radial solutions of the focusing, energy-critical wave equation
• The effect of linear perturbations on the Yamabe problem
• Convergence of the Yamabe flow in dimension 6 and higher
• Examples of non-isolated blow-up for perturbations of the scalar curvature equation on non-locally conformally flat manifolds
• Bubble towers in the ancient solution of energy-critical heat equation
• Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity
• Blow-up solutions for asymptotically critical elliptic equations on Riemannian manifolds
• The Yamabe problem
• The yamabe flow on locally conformally flat manifolds with positive ricci curvature
• Formal Asymptotics of Bubbling in the Harmonic Map Heat Flow
• Convergence of the Yamabe flow for large energies
• YAMABE TYPE EQUATIONS ON THREE DIMENSIONAL RIEMANNIAN MANIFOLDS
• Stable Blowup Dynamics for the 1‐Corotational Energy Critical Harmonic Heat Flow
• Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains
• Finite Time Blowup for the Nematic Liquid Crystal Flow in Dimension Two
• Clustering Phenomena for Linear Perturbation of the Yamabe Equation
• Optimal boundary regularity for fast diffusion equations in bounded domains
• Bubbling and extinction for some fast diffusion equations in bounded domains
• Extinction behavior for the fast diffusion equations with critical exponent and Dirichlet boundary conditions