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Transport, Fluids and Mixing

Regularity of the flow of 2d autonomous divergence-free vector fields

speaker: Elio Marconi (École polytechnique fédérale de Lausanne )

abstract: We consider the regular Lagrangian flow $X$ associated to a bounded divergence-free vector field $b$ with Sobolev or BV regularity. We prove a Lusin-Lipschitz regularity result for $X$ and we show that the Lipschitz constant grows at most linearly in time. We moreover discuss under which conditions, the flow $X$ inherits the Sobolev or BV regularity of $b$. Part of the work is done in collaboration with Paolo Bonicatto.

timetable:
Mon 24 Jan, 16:30 - 17:00,
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