Local existence and uniqueness in the largest critical space for a surface growth model

  • We show the existence and uniqueness of solutions (either local or global for small data) for an equation arising in different aspects of surface growth. Following the work of Koch and Tataru we consider spaces critical with respect to scaling and we prove our results in the largest possible critical space such that weak solutions are defined. The uniqueness of global weak solutions remains unfortunately open, unless the initial conditions are sufficiently small.

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Author:Dirk BlömkerORCiDGND, Marco RomitoORCiD
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1367
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2010-03)
Year of first Publication:2010
Publishing Institution:Universität Augsburg
Contributing Corporation:Universita di Firenze, Dipartimento di Matematica
Release Date:2010/03/24
Tag:surface growth; critical space; uniqueness; regularity
GND-Keyword:Parabolische Differentialgleichung; Partielle Differentialgleichung; Nichtlineare partielle Differentialgleichung
Erschienen in Nonlinear Differential Equations and Applications NoDEA, 19, 3, S. 365-381, https://doi.org/10.1007/s00030-011-0133-2
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand