Abstract We study the Kuramoto-Sivashinsky equation (KSE) in scalar form on the two-
dimensional torus with and without advection by an incompressible vector field. We prove …

We introduce the planar helical flows on three dimensional torus and study the dissipation
enhancement of such flows. We then use such flows as transport flows to solve the three …

We address the global existence of solutions for the 2D Kuramoto-Sivashinsky equations in
a periodic domain 0, L_1 * 0, L_2 0, L 1× 0, L 2 with initial data satisfying ‖ u_0 ‖ _ L^ 2 ≤ …

We propose an approximate model for the 2D Kuramoto–Sivashinsky equations (KSE) of
flame fronts and crystal growth. We prove that this new'calmed'version of the KSE is globally …

Abstract 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 …

There is little analytical theory for the behavior of solutions of the Kuramoto–Sivashinsky
equation in two spatial dimensions over long times. We study the case in which the spatial …

Abstract We consider the Kuramoto–Sivashinsky equation in two space dimensions. We
establish the first proof of global existence of solutions in the presence of a linearly growing …

Abstract The Kuramoto–Sivashinsky equations (KSE) arise in many diverse scientific areas,
and are of much mathematical interest due in part to their chaotic behavior, and their …

We propose and prove several regularity criteria for the 2D and 3D Kuramoto–Sivashinsky
equation, in both its scalar and vector forms. In particular, we examine integrability criteria for …

A Kuramoto–Sivashinsky equation in two space dimensions arising in thin film flows is
considered on doubly periodic domains. In the absence of dispersive effects, this anisotropic …