5 problems

Let $\mathcal{A}_L$ be the global attractor of the one-dimensional Kuramoto–Sivashinsky equation with periodic boundary conditions of period $L$, and let $d_H(\mathcal{A}_L)$ and…

Yakhot's conjecture. In the hydrodynamic limit, the probability distribution of the Kuramoto–Sivashinsky equation may be mimicked by that of the noise-driven inviscid Burgers equat…

Let $u$ be a solution of the Kuramoto–Sivashinsky equation, let $v$ be the convolution of $u_x$ with a normalized Gaussian in $x$ of standard deviation $2$, and define a stripe to…

Let the Kuramoto–Sivashinsky equation be considered in a transient regime, and let the Kardar–Parisi–Zhang equivalence class denote the universality class characterized by its scal…

Let $u$ solve the differentiated periodic Kuramoto–Sivashinsky equation … with period $2L$ and initial data $u(0,x)=u_0(x)$. Optimal attracting-norm estimates. Based on numerical s…