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Abstract:

The method of convex integration originally comes from differential geometry. It was first used in 1954 in Nash's solution to the isometric embedding problem and was later brought to fluid dynamics. In this talk we will first visit some of the well-known results achieved by convex integration and then turn to an application of a concrete convex integration scheme, namely the failure of the chainrule for the divergence of vector fields. For given scalar functions $\beta$ and $f$, the aim is to construct via convex integration a Sobolev vector field $v$ and a scalar $L^p$-function $\rho$ such that the product is divergence-free, but $\div(\beta(\rho)v) = f.$ Finally, we discuss some possible generalisations and problems that may occur.

Wann?

02. Dezember 2021, 14:00-15:30

Wo?

TU Darmstadt FB Mathematik AG Analysis
S2/15 Raum 51
Schlossgartenstr. 7