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SUMMARY:On the well-posedness theory for higher-order (d)NLS hierarchy equ
 ations
DTSTART:20260626T121500Z
DTEND:20260626T134500Z
DTSTAMP:20260526T042400Z
UID:indico-event-1342@math-events.uni-bonn.de
DESCRIPTION:Speakers: Joseph Adams (Heinrich-Heine-Universität Düsseldor
 f)\n\nAbstract:\nComplete integrability of dispersive PDEs has become a ce
 ntral property in the well-posedness and stability analysis of PDEs that p
 ossess this property\, usually yielding an infinite number of conserved qu
 antities and often explicit families of solutions available. Classical exa
 mples of such equations are the cubic nonlinear Schrödinger (NLS) equatio
 n and its close relative the derivative nonlinear Schrödinger (dNLS) equa
 tion. \nWith both of these equations there are associated\, higher-order\
 , PDEs that are derived from their conservation laws - so called integrabl
 e hierarchies. In this talk we review the recent developments in the well-
 posedness theory of equations in these hierarchies\, while not explicitly 
 relying on their complete integrability. We will be covering said equation
 's derivation\, (multilinear refinements of) Strichartz estimates leading 
 to low-regularity well-posedness\, as well as complementary ill-posedness 
 results establishing optimality. We conclude with a discussion of some ope
 n questions related to the presented material. \n \n\nhttps://math-event
 s.uni-bonn.de/event/1342/
LOCATION:Endenicher Allee 60\, Seminarraum 0.011 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1342/
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