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Long‐time asymptotics of the Navier‐Stokes equation in ℝ 2 and ℝ 3
Author(s) -
Gallay T.,
Wayne C.E.
Publication year - 2006
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.200510260
Subject(s) - vorticity , stability (learning theory) , navier–stokes equations , vortex , mathematics , burgers' equation , kinetic theory , mathematical analysis , dynamical systems theory , classical mechanics , statistical physics , physics , differential equation , mechanics , computer science , theoretical physics , compressibility , quantum mechanics , machine learning
In this paper we survey our recent research about how one can combine ideas from dynamical systems theory and kinetic theory to describe the long‐time behavior of solutions of the Navier‐Stokes equations. In two dimensions this leads to a very complete description of the behavior of solutions whose initial vorticity is at least slightly localized. In three dimensions it gives a better understanding of the existence and stability of the Burgers vortex and its variants.