We consider the initial value problem (IVP) associated to a system consisting modiﬁed Korteweg-de Vries (mKdV) type equations and prove the local well-posedness results for given data in low regularity Sobolev spaces Hs(R)×Hs(R), s > −1 2. We also prove that the local well-posedness result is sharp in two diﬀerent ways, viz., for s < −1 2 the key trilinear estimates used in the proof of the local wellposedness theorem fail to hold, and the ﬂow-map that takes initial data to the solution fails to be C3 at the origin.
Xavier Carvajal (IM-UFRJ)
Data do Evento:
sexta-feira, 08 de Fevereiro de 2019 - 13:43 até terça-feira, 12 de Fevereiro de 2019 - 17:00