Related papers: Global existence and analyticity for the 2D Kuramo…
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 anisotropic, i.e. are results of thin-domain type. In the spatially…
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 has a finite number of critical points and there are…
We prove existence of solutions to the Kuramoto-Sivashinsky equation with low-regularity data, in function spaces based on the Wiener algebra and in pseudomeasure spaces. In any spatial dimension, we allow the data to have its…
A certain model for epitaxial film growth has recently attracted attention, with the existence of small global solutions having being proved in both the case of the n-dimensional torus and free space. We address a regularity question for…
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 local existence of mild solutions for arbitrary data in L2. We then study…
This report provides an investigation into solving the Kuramoto-Sivashinsky equation in two spatial dimensions (2DKS) using a pseudo-spectral method on various rectangular periodic domains. The Kuramoto-Sivashinsky equation is a fluid…
A non linear Ito equation in a Hilbert space is studied by means of Girsanov theorem. We consider a non linearity of polynomial growth in suitable norms, including that of quadratic type which appears in the Kuramoto-Sivashinsky equation…
In this article we study the solution of the Kuramoto-Sivashinsky equation (for surface erosion or surface growth) on a bounded interval subject to a random forcing term. We show that a unique solution to the equation exists for all time…
In this article, we consider a non-local variant of the Kuramoto-Sivashinsky equation in three dimensions (2D interface). Besides showing the global wellposedness of this equation we also obtain some qualitative properties of the solutions.…
In this article, some elementary observations are made regarding the behavior of solutions to the two-dimensional curl-free Burgers equation which suggest the distinguished role played by the scalar divergence field in determining the…
Initial-boundary value problems for the $n$-dimensional ($n$ is a natural number from the interval [2,7]) Kuramoto-Sivashinsky equation posed on smooth bounded domains in $\mathbb{R}^n$ were considered. The existence and uniqueness of…
This paper presents new findings concerning the dynamics of the slow height variations in surfaces produced by the two-dimensional isotropic Kuramoto-Sivashinsky equation with an additional nonlinear term. In addition to the disordered…
The conserved Kuramoto-Sivashinsky equation is considered as the evolution equation of amorphous thin film growth in one- and in two-dimensions. The role of the nonlinear term $\Delta (\ | \nabla u\ | ^{2})$ and the properties of the…
We consider the completely resonant defocusing non-linear Schr\"odinger equation on the two dimensional torus with any analytic gauge invariant nonlinearity. Fix $s>1$. We show the existence of solutions of this equation which achieve…
In this paper we prove the existence of solutions to the cubic NLS equation with convolution potentials on two dimensional irrational tori undergoing an arbitrarily large growth of Sobolev norms as time evolves. Our results apply also to…
We consider here the local existence of strong solutions for the Zakharov-Kuznestov (ZK) equation posed in a limited domain (0,1)_{x}\times(-pi /2, pi /2)^d, d=1,2. We prove that in space dimensions 2 and 3, there exists a strong solution…
We consider the Euler equations on the two-dimensional torus and construct invariant measures for the dynamics of these equations, concentrated on sufficiently regular Sobolev spaces so that strong solutions are also known to exist. The…
We consider the cubic defocusing nonlinear Schr\"odinger equation in the two dimensional torus. Fix $s>1$. Colliander, Keel, Staffilani, Tao and Takaoka proved in \cite{CollianderKSTT10} the existence of solutions with $s$-Sobolev norm…
We show the existence and uniqueness of solutions (either local or global for small data) for an equation arising in different aspects of surface growth. Following the work of Koch and Tataru we consider spaces critical with respect to…
We study constrained 2-dimensional Navier-Stokes Equations driven by a multiplicative Gaussian noise in the Stratonovich form. In the deterministic case [4] we showed the existence of global solutions only on a two dimensional torus and…