Lack of uniqueness for weak solutions of the incompressible porous media equation

Details Lack of uniqueness for weak solutions of the incompressible porous media equation Lack of uniqueness for weak solutions of the incompressible porous media equation

2009-12-16

arxiv.org/abs/0912.3210v1

Mathematics

Analysis of PDEs

23 pages, 2 fugures

Scientific paper

In this work we consider weak solutions of the incompressible 2-D porous
media equation. By using the approach of De Lellis-Sz\'ekelyhidi we prove
non-uniqueness for solutions in $L^\infty$ in space and time.

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