Well-posedness of the supercritical Lane–Emden heat flow in Morrey spaces

DOI10.1051/COCV/2016041zbMath1364.35129arXiv1511.07685OpenAlexW2277367584MaRDI QIDQ2835363

Michael Struwe, Simon Blatt

Publication date: 2 December 2016

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.07685

zbMATH Keywords

nonlinear parabolic equationsMorrey spacessupercritical Lane-Emdenwell-posedness of initial-boundary value problem

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial-boundary value problems for higher-order parabolic equations (35K35) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (2)

Global, decaying solutions of a focusing energy-critical heat equation in \(\mathbb{R}^4\) ⋮ Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in \(\mathbb{R}^n\)

Cites Work

• The heat flow with a critical exponential nonlinearity
• Boundary regularity for the supercritical Lane-Emden heat flow
• Classification of type I and type II behaviors for a supercritical nonlinear heat equation
• Complete blow-up after \(T_{\max}\) for the solution of a semilinear heat equation
• Existence and non-existence of global solutions for a semilinear heat equation
• A note on Riesz potentials
• A nonlinear heat equation with singular initial data
• Quasilinear Dirichlet problems driven by positive sources
• Analysis on Morrey Spaces and Applications to Navier-Stokes and Other Evolution Equations
• Continuation of blowup solutions of nonlinear heat equations in several space dimensions
• An Analytic Framework for the Supercritical Lane-Emden Equation and its Gradient Flow
• On the growth of solutions of quasi‐linear parabolic equations
• Well-posedness for the Navier-Stokes equations

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