Long time behavior of solutions for a damped Benjamin-Ono equation

Louise Gassot

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arXiv · 2010.05520

Long time behavior of solutions for a damped Benjamin-Ono equation

Louise Gassot

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Abstract

We consider the Benjamin-Ono equation on the torus with an additional damping term on the smallest Fourier modes (cos and sin). We first prove global well-posedness of this equation in $L^2_{r,0}(\mathbb{T})$. Then, we describe the weak limit points of the trajectories in $L^2_{r,0}(\mathbb{T})$ when time goes to infinity, and show that these weak limit points are strong limit points. Finally, we prove the boundedness of higher-order Sobolev norms for this equation. Our key tool is the Birkhoff map for the Benjamin-Ono equation, that we use as an adapted nonlinear Fourier transform.

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Louise Gassot. 2020-10-12. Long time behavior of solutions for a damped Benjamin-Ono equation. https://arxiv.org/abs/2010.05520

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