Seminar Analysis and Mathematical Physics: Stefano Modena (GSSI L'Aquila)

On some typicality and density results for non smooth vector fields

For the linear continuity equation associated to incompressible vector fields we show that the set of vector fields in $L^q_x$, $q<\infty$, for which the continuity equation admits a unique distributional solution in $L^{q’}_x$ (for all initial data) is generic in the Baire category sense, whereas its complement, as well as some particular subset of it, is dense. Analog results for the ODE associated to continuous vector fields will be also discussed. (Joint work with Francesco Cianfrocca).

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