Existence of Weak Solutions for the Incompressible Euler Equations

Details Existence of Weak Solutions for the Incompressible Euler Equations Existence of Weak Solutions for the Incompressible Euler Equations

2011-02-17

arxiv.org/abs/1102.3614v1

Mathematics

Analysis of PDEs

5 pages

Scientific paper

Using a recent result of C. De Lellis and L. Sz\'{e}kelyhidi Jr. we show that, in the case of periodic boundary conditions and for dimension greater or equal 2, there exist infinitely many global weak solutions to the incompressible Euler equations with initial data $v_0$, where $v_0$ may be any solenoidal $L^2$-vectorfield. In addition, the energy of these solutions is bounded in time.

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