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It is known since the pioneering works of Scheffer and Shnirelman that there are nontrivial distributional solutions to the Euler equations which are compactly supported in space and time. Obviously these solutions do not respect the classical conservation law for the total kinetic energy and they are therefore very irregular. In recent joint works we have… (More)

- A. Choffrut, L. Székelyhidi
- SIAM J. Math. Analysis
- 2014

We show the existence of Hölder continuous solution of Boussinesq equations in whole space which has compact support both in space and time.

In this note we prove that if K is a compact set of m × n matrices containing an isolated point X with no rank-one connection into the convex hull of K \ {X}, then the rank-one convex hull separates as K rc = K \ {X} rc ∪ {X}. This is an extension of a result of P. Pedregal, which holds for 2 × 2 matrices.

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