Low regularity conservation laws for the Camassa-Holm equation and the Fokas-Lenells equation
Prof. Minjie Shan
2023-07-31 15:00-16:00
MCM110
Speaker: Prof. Minjie Shan (Minzu University of China)Time: 15:00-16:00 July 31, 2023 (Monday)
Place: MCM110
Title: Low regularity conservation laws for the Camassa-Holm equation and the Fokas-Lenells equation
Abstract: In this talk, we will show low regularity conservation laws for the Camassa-Holm equation and the Fokas-Lenells equation in Besov spaces both on the line and on the circle. Analogous to the derivation of the Camassa-Holm equation from the KdV equation, the Fokas-Lenells equation is an integrable generalization of the nonlinear Schrodinger equation (NLS). The inverse scattering method usually is a useful tool to study the long-time asymptotic behavior of completely integrable systems. However, there are major technical difficulties to use inverse scattering techniques in unweighted Sobolev spaces. For instance, on the line the decay of the data is insufficient when inverse scattering method is applied. The method we use here is introduced by Killip, Visan and Zhang for completely integrable dispersive PDEs with negative regularity. Specifically, we utilize the power series expansion of the perturbation determinant associated to the Lax pair to derive low regularity a-priori estimates.
