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On regularity properties of a surface growth model

Part of: Incompressible viscous fluids Thin bodies, structures Parabolic equations and systems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  09 March 2021

Jan Burczak Open the ORCID record for Jan Burczak [Opens in a new window] ,
Wojciech S. Ożański Open the ORCID record for Wojciech S. Ożański [Opens in a new window]  and
Gregory Seregin
Jan Burczak
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland and Mathematisches Institut, Universität Leipzig, Augustusplatz 10, D-04109Leipzig, Germany (burczak@math.uni-leipzig.de)
Wojciech S. Ożański
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA90089, USA (ozanski@usc.edu)
Gregory Seregin
Affiliation:
Oxford University, UK and St Petersburg Department of Steklov Mathematical Institute, RAS, Russia (seregin@maths.ox.ac.uk)
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Abstract

We show local higher integrability of derivative of a suitable weak solution to the surface growth model, provided a scale-invariant quantity is locally bounded. If additionally our scale-invariant quantity is small, we prove local smoothness of solutions.

Keywords

Surface growth modelpartial regularitylocal higher integrabilitysingular setbox-counting dimensionHausdorff dimension

MSC classification

Primary: 35K25: Higher-order parabolic equations
Secondary: 35K55: Nonlinear parabolic equations 76D03: Existence, uniqueness, and regularity theory 74K35: Thin films 35Q35: PDEs in connection with fluid mechanics 35Q30: Navier-Stokes equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 6 , December 2021 , pp. 1869 - 1892
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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