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Global well‐posedness of the aggregation equation with supercritical dissipation in Besov spaces
Author(s) -
Wu G.,
Zhang Q.
Publication year - 2013
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200167
Subject(s) - supercritical fluid , dissipation , fourier transform , besov space , mathematics , mathematical analysis , physics , interpolation space , functional analysis , thermodynamics , chemistry , biochemistry , gene
In this paper, we study the supercritical aggregation equation. We prove the global well‐posedness for small initial data lying in Besov spaces and the local well‐posedness for arbitrary initial data. The Fourier localization technique and the Littlewood‐Paley theory are the main tools used in the proof.