Young Measures Generated by Ideal Incompressible Fluid Flows

Details Young Measures Generated by Ideal Incompressible Fluid Flows Young Measures Generated by Ideal Incompressible Fluid Flows

2011-01-18

arxiv.org/abs/1101.3499v2

Mathematics

Analysis of PDEs

36 pages, 2 figures; some typos corrected, in particular in the statement of Theorem 2

Scientific paper

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.

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