Microglobal analysis of the Euler equations

DOI10.1007/s00021-005-0167-5zbMath1080.76011OpenAlexW2021958547MaRDI QIDQ814409

Alexander I. Shnirelman

Publication date: 7 February 2006

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00021-005-0167-5

zbMATH Keywords

volume-preserving diffeomorphismsparadifferential operatorsquasiruled Fredholm exponential map

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

Related Items (12)

Local ill-posedness of the incompressible Euler equations in \(C^1\) and \(B^1_{\infty,1}\) ⋮ Fredholm properties of Riemannian exponential maps on diffeomorphism groups ⋮ The exponential map of the group of area-preserving diffeomorphisms of a surface with boundary ⋮ The Schwarz-Milnor lemma for braids and area-preserving diffeomorphisms ⋮ The \(L^p\)-diameter of the group of area-preserving diffeomorphisms of \(S^2\) ⋮ Paralinearization of the Muskat equation and application to the Cauchy problem ⋮ On paracomposition and change of variables in paradifferential operators ⋮ On the Cauchy problem for dispersive Burgers type equations ⋮ Geometric hydrodynamics in open problems ⋮ Singularity formation in the incompressible Euler equation in finite and infinite time ⋮ Regularity results on the flow maps of periodic dispersive Burgers type equations and the gravity-capillary equations ⋮ Surface tension of multi-phase flow with multiple junctions governed by the variational principle

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