Optimal regularity for linear advection equations: A Littlewood-Paley approach.

speaker: Christian Seis (Universität Münster)

abstract: It has been established in recent years that the regularity propagated by linear transport equations is rather poor: When the advecting velocity field is merely Sobolev regular, then the control on any (fractional) derivative might get lost instantaneously and the maximal regularity that is preserved during the evolution is only of logarithmic order, measured in terms of suitable Gagliardo-Sobolev norms. In this talk, I will describe an alternative approach to optimal regularity estimates based on Littlewood-Paley theory, thus analyzing the maximal regularity control in frequency space. Joint work with David Meyer.

timetable:
Tue 25 Jan, 11:00 - 11:50,
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