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On the non-uniqueness of weak solution of the Euler equations. (English) Zbl 0881.35096
The author considers fluid flows on the two-dimensional torus and constructs a discontinuous unbounded weak solution \(u(x,t)\in L^2\) of the incompressible homogeneous Euler equations, having a compact support in time. This means, in particular, that the weak solution with given (zero) initial velocity is not unique, and that the kinetic energy is not constant in time, as for the Hölder continuous solutions of the Euler equations. The proof uses the physical idea of inverse energy cascade from the two-dimensional turbulence theory.
Reviewer: O.Titow (Berlin)

35Q35 PDEs in connection with fluid mechanics
76B99 Incompressible inviscid fluids
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