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Weak solution of incompressible Euler equations with decreasing energy. (English. Abridged French version) Zbl 0913.35110
Summary: Weak solution of incompressible Euler equations are \(L^2\)-vector fields, satisfying integral relations, which express the mass and momentum balance. They are believed to describe the turbulent fluid motion at high Reynolds numbers. We justify this conjecture by constructing a weak solution with decreasing kinetic energy. The construction is based on generalized flows, introduced by Y. Brenier.
MSC:
35Q35 PDEs in connection with fluid mechanics
76B99 Incompressible inviscid fluids
35D05 Existence of generalized solutions of PDE (MSC2000)
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