Title
Smoothing effect for third order operators with variable coefficients
Abstract
The aim of the talk is to study the smoothing effect of some variable coefficient operators of the form $\partial_t-iA$, where $A$ is a (pseudo)differential operator of order $m=2,3$. The class under consideration includes KdV-type and ultrahyperbolic Schrödinger operators with both constant and variable coefficients, and generalizes a broad class of dispersive equations.
We establish homogeneous and inhomogeneous smoothing estimates and apply them to obtain well-posedness results for certain nonlinear initial value problems involving derivative nonlinearities.
Finally, we examine the connection with the nontrapping condition for the bicharacteristic curves of the principal symbol of the operator in question.
We establish homogeneous and inhomogeneous smoothing estimates and apply them to obtain well-posedness results for certain nonlinear initial value problems involving derivative nonlinearities.
Finally, we examine the connection with the nontrapping condition for the bicharacteristic curves of the principal symbol of the operator in question.
Please note that the seminar will take place in person in room 140 of Huxley Building.