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On the nonuniqueness of weak solutions of the Euler equation. (English) Zbl 0909.35109
Author’s abstract: “Weak solution of the Euler equations \[ {\partial u\over\partial t}+ (u,\nabla)u+\nabla p= 0,\quad\nabla u= 0 \] is defined as an \(L^2\)-vector field satisfying the integral relations expressing the mass and momentum balance. Their general nature has been quite unclear. In this work an example of a weak solution on a two-dimensional torus is constructed that is identically zero outside a finite time interval. This example is simpler and more transparent than the previous example of V. Scheffer [J. Geom. Anal. 3, 343-401 (1993; Zbl 0836.76017)]”.

MSC:
35Q35 PDEs in connection with fluid mechanics
35D99 Generalized solutions to partial differential equations
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