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On the Cauchy problem for quasi-linear Schrödinger-type equations on the circle

Felice Iandoli
Institution: 
SISSA
Location: 
A-133
Schedule: 
Friday, February 23, 2018 - 14:00
Abstract: 

I discuss local in time well-posedness for a large class of quasi-linear Hamiltonian, or parity preserving, Schrödinger equations on the circle. Using para-differential tools I show that the system can be reduced to another one with symbols which, at positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solution. Time permitting I will speak about a recent work in which I prove almost global existence for small amplitude solutions of such equations. These are joint works with Roberto Feola.

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