Abstract
Chapter 7 is the natural continuation of the previous chapter: The diffusion term is removed, leading to the study of the Euler system for inviscid incompressible fluids. Here, we state local (in dimension d≥3) and global (in dimension two) well-posedness results for data in general Besov spaces. In particular, we study the case where the data belong to Besov spaces for which the embedding in the set of Lipschitz functions is critical. In the two-dimensional case, we also give results concerning the inviscid limit. We stress the case of data with (generalized) vortex patch structure.
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© 2011 Springer-Verlag Berlin Heidelberg
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Bahouri, H., Chemin, JY., Danchin, R. (2011). Euler System for Perfect Incompressible Fluids. In: Fourier Analysis and Nonlinear Partial Differential Equations. Grundlehren der mathematischen Wissenschaften, vol 343. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16830-7_7
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DOI: https://doi.org/10.1007/978-3-642-16830-7_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16829-1
Online ISBN: 978-3-642-16830-7
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