4 problems

Convergence conjecture. The solution $f(t)$ converges to the global equilibrium $f_{\infty}$ as $t\to\infty$; moreover, the convergence rate should be estimated.

Let $D_{xx}$ denote the effective diffusion coefficient in the $x$ direction for the stochastic dynamics described above, with $uin(0,1)$ and compressibility parameter…

Let $p=p(n_0)\in(0,1)$ be the exponent in the decay rate from the preceding theorem, where $n_0$ denotes the order of the first nonvanishing derivative of the shear profile. The en…

The model is considered on a torus, with natural modifications consisting of bounded domains with specular-reflection boundary conditions or the whole space equipped with confining…