Global Existence for the Two-dimensional Kuramoto-Sivashinsky equation with a Shear Flow

no code implementations • 4 Mar 2021 • Michele Coti Zelati, Michele Dolce, Yuanyuan Feng, Anna L. Mazzucato

We consider the Kuramoto-Sivashinsky equation (KSE) on the two-dimensional torus in the presence of advection by a given background shear flow.

Analysis of PDEs 35K25, 35K58, 76E06, 76F25

Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation

no code implementations • 2 Feb 2019 • Yuanyuan Feng, Tingran Gao, Lei LI, Jian-Guo Liu, Yulong Lu

Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon.

Stochastic Optimization