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Applied and computational Analysis Seminars

Low regularity approximations to dispersive equations

With Yvonne Bronsard (Sorbonne Université)

Low regularity approximations to dispersive equations

In this talk we will discuss low regularity approximations to nonlinear dispersive equations, both in the case of deterministic and random initial data.
We will put forth a novel time discretization to the nonlinear Schrödinger equation, allowing for a low regularity approximation while maintaining good long-time preservation of the mass and energy on the discrete level. Higher order extensions will be presented, following new techniques based on decorated trees series analysis inspired by singular SPD Es. Part of the work presented here is in collaboration with Yvain Bruned and Katharina Schratz.

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