Quasi-invariance of Gaussian measures for the periodic Benjamin-Ono-BBM equation

周期Benjamin-Ono-BBM方程的改进的拟不变性结果

Improved quasi-invariance result for the periodic Benjamin-Ono-BBM equation

本文将周期Benjamin-Ono-BBM方程流下Gaussian测度拟不变性的结果扩展至全局适定的全范围，通过结合现有方法与迭代论证克服色散临界困难，获得了传输密度的长时间高阶可积性界限。

Construction of a Gibbs measure associated to the periodic Benjamin-Ono equation

We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the ODE's which correspond to the projection of the Benjamin-Ono equation, posed on the circle, on the first N>>1 modes in the trigonometric bases.

方差爆破之外色散偏微分方程的概率适定性 I：Benjamin-Bona-Mahony 方程

Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation

该研究拓展非线性色散PDE概率适定性理论至方差爆破外，以BBM方程为对象，通过两种重整化方法证明解的依分布收敛性，且结果适用于任意低正则高斯初值，还推广到分数阶噪声驱动情形。