For some deterministic nonlinear PDEs on the torus whose solutions may blow up in finite
time, we show that, under suitable conditions on the nonlinear term, the blow-up is delayed …

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 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 …

Our goal in this paper is to investigate ergodicity of white-forced Kuramoto-Sivashinsky
equation (KSE) on the whole line. Under the assumption that sufficiently many directions of …

We study enhanced dissipation due to the combined effect of diffusion or hyperdiffusion and
advection by an incompressible flow with circular or cylindrical symmetry in 2 and 3 space …

We consider following fourth-order parabolic equation with gradient nonlinearity on the two-
dimensional torus with and without advection of an incompressible vector field in the case …

In a general domain, we discuss an initial value problem for the symmetry generalized MM‐
coupled system of fourth‐order parabolic equations with space–time‐dependent diffusion …

This study undertakes the challenging task of unraveling the intricacies embedded in the
integrable Kuralay equation, a cornerstone in the field of mathematical physics. Specifically …

This paper uses Z transformations to obtain the general solutions of a large number of
second-order, third-order and fourth-order linear partial differential equations for the first …