论文标题
抑制benjamin-ono方程的解决方案的长时间行为
Long time behavior of solutions for a damped Benjamin-Ono equation
论文作者
论文摘要
我们考虑了圆环上的本杰明·奥诺方程，并在最小的傅立叶模式（cos和sin）上具有附加的阻尼术语。我们首先在$ l^2_ {r，0}（\ mathbb {t}）$中证明了该方程的全局良好性。然后，我们描述了$ l^2_ {r，0}（\ Mathbb {t}）$中的轨迹的弱限制点，当时间到达无限时，并证明这些弱限制点是强限点。最后，我们证明了该方程式的高阶Sobolev规范的界限。我们的关键工具是Benjamin-Ono方程的Birkhoff地图，我们用作适应的非线性傅立叶变换。
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.
