Existence of Weak Solutions for the Incompressible Euler Equations
Abstract
Using a recent result of C. De Lellis and L. Sz\'ekelyhidi 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 v0, where v0 may be any solenoidal L2-vectorfield. In addition, the energy of these solutions is bounded in time.
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