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- W3092164803 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." @default.
- W3092164803 created "2020-10-15" @default.
- W3092164803 creator A5056915080 @default.
- W3092164803 date "2020-10-09" @default.
- W3092164803 modified "2023-09-25" @default.
- W3092164803 title "Long time behavior of solutions for a damped Benjamin-Ono equation" @default.
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- W3092164803 hasPublicationYear "2020" @default.
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