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On the well-posedness of the incompressible Euler equation


Inci, Hasan. On the well-posedness of the incompressible Euler equation. 2013, University of Zurich, Faculty of Science.

Abstract

In this thesis we prove that the homogeneous incompressible Euler equation of hydrodynamics on the Sobolev spaces H s (Rn ), n ≥ 2 and s > n/2 + 1, can be ex- pressed as a geodesic equation on an infinite dimensional manifold. As an application of this geometric formulation we prove that the solution map of the incompressible Euler equation, associating intial data in H s (Rn ) to the corresponding solution at time t > 0, is nowhere locally uniformly continuous and nowhere differentiable.

Abstract

In this thesis we prove that the homogeneous incompressible Euler equation of hydrodynamics on the Sobolev spaces H s (Rn ), n ≥ 2 and s > n/2 + 1, can be ex- pressed as a geodesic equation on an infinite dimensional manifold. As an application of this geometric formulation we prove that the solution map of the incompressible Euler equation, associating intial data in H s (Rn ) to the corresponding solution at time t > 0, is nowhere locally uniformly continuous and nowhere differentiable.

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Additional indexing

Item Type:Dissertation (monographical)
Referees:Kappeler Thomas, De Lellis Camillo
Communities & Collections:UZH Dissertations
Dewey Decimal Classification:Unspecified
Language:English
Place of Publication:Zürich
Date:2013
Deposited On:04 Apr 2019 09:35
Last Modified:15 Apr 2021 15:01
Number of Pages:92
OA Status:Green

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