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• W3197426586 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.
• W3197426586 created "2021-09-13" @default.
• W3197426586 creator A5056915080 @default.
• W3197426586 date "2021-09-02" @default.
• W3197426586 modified "2023-09-25" @default.
• W3197426586 title "Long time behavior of solutions for a damped Benjamin–Ono equation" @default.
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• W3197426586 doi "https://doi.org/10.1007/s00209-021-02849-w" @default.
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