Conferences and seminars
On decay and regularity properties of solutions to the Benjamin-Ono equation
Bilde
Filipe Linares, Professor @ Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil.
Abstract:
In this talk we will discuss recent results regarding persistence properties of the solution of the Benjamin-Ono (BO) equation in weighted Sobolev spaces. In particular, we will show that for \beta<7/2, the solution u(x,t) of the BO equation remains in the space L^2(|x|^{2\beta} dx) if and only if its data u(x,0) belongs to this space and it is regular enough, i.e. u_0 in the space H^{\beta}(\mathbb R). This is a joint work with Gustavo Ponce (UCSB, USA).