Well-posedness of the supercritical Lane–Emden heat flow in Morrey spaces
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1370-1381.

For any smoothly bounded domain Ω n , n3, and any exponent p>2 * =2n/(n-2) we study the Lane–Emden heat flow u t -Δu=|u| p-2 u on Ω×]0,T[ and establish local and global well-posedness results for the initial value problem with suitably small initial data u| t=0 =u 0 in the Morrey space L 2,λ (Ω) for suitable T, where λ=4/(p-2). We contrast our results with results on instantaneous complete blow-up of the flow for certain large data in this space, similar to ill-posedness results of Galaktionov–Vazquez for the Lane–Emden flow on n .

DOI : 10.1051/cocv/2016041
Classification : 35K55
Mots clés : Nonlinear parabolic equations, well-posedness of initial-boundary value problem
Blatt, Simon 1 ; Struwe, Michael 2

1 Fachbereich Mathematik, Universität Salzburg, Hellbrunner Str. 34, 5020 Salzburg, Austria
2 Departement Mathematik, ETH-Zürich, 8092 Zürich, Switzerland
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     title = {Well-posedness of the supercritical {Lane{\textendash}Emden} heat flow in {Morrey} spaces},
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Blatt, Simon; Struwe, Michael. Well-posedness of the supercritical Lane–Emden heat flow in Morrey spaces. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1370-1381. doi : 10.1051/cocv/2016041. http://archive.numdam.org/articles/10.1051/cocv/2016041/

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