Young Measures Generated by Ideal Incompressible Fluid Flows

Abstract

In their seminal paper "Oscillations and concentrations in weak solutions of the incompressible fluid equations", R. DiPerna and A. Majda introduced the notion of measure-valued solution for the incompressible Euler equations in order to capture complex phenomena present in limits of approximate solutions, such as persistence of oscillation and development of concentrations. Furthermore, they gave several explicit examples exhibiting such phenomena. In this paper we show that any measure-valued solution can be generated by a sequence of exact weak solutions. In particular this gives rise to a very large, arguably too large, set of weak solutions of the incompressible Euler equations.

35 pages. Final revised version. To appear in Arch. Ration. Mech. Anal

References in corpus (1)

• Existence of Weak Solutions for the Incompressible Euler Equations

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• Computation of measure-valued solutions for the incompressible Euler equations
• Weak stablity and closure in turbulence
• Oscillation and concentration in sequences of PDE constrained measures
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• Probabilistic Descriptions of Fluid Flow: A Survey
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• Young-measure solutions for multidimensional systems of conservation laws
• Finite element formulation of general boundary conditions for incompressible flows