66 citations · 171 across the 35 of their papers we have counts for
4 papers · 1 filter
Approximate Solutions to Second-Order Parabolic Equations: evolution systems and discretization
Wen Cheng, Anna L. Mazzucato, Victor Nistor
We study the discretization of a linear evolution partial differential equation when its Green function is known. We provide error estimates both for the spatial approximation and…
Growth of Sobolev norms and loss of regularity in transport equations
Gianluca Crippa, Tarek Elgindi, Gautam Iyer +1
We consider transport of a passive scalar advected by an irregular divergence free vector field. Given any non-constant initial data , $d\g…
Global Existence for the Two-dimensional Kuramoto-Sivashinsky equation with a Shear Flow
Michele Coti Zelati, Michele Dolce, Yuanyuan Feng +1
We consider the Kuramoto-Sivashinsky equation (KSE) on the two-dimensional torus in the presence of advection by a given background shear flow. Under the assumption that the shear…
Global solutions of the two-dimensional Kuramoto-Sivashinsky equation with a linearly growing mode in each direction
David M. Ambrose, Anna L. Mazzucato
In two spatial dimensions, there are very few global existence results for the Kuramoto-Sivashinsky equation. The majority of the few results in the literature are strongly anisotr…