Related papers: KdV Preserves White Noise
We study here the water-waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known, that for such regimes, a generalization of the KdV…
We study equations like the Mackey-Glass equations and Nicholson's blowflies equation, each perturbed by a (small) multiplicative noise term. Solutions to these stochastic negative feedback systems persist globally and are bounded above in…
This paper is concerned with stochastic systems whose state is a diffusion process governed by an Ito stochastic differential equation (SDE). In the framework of a nominal white-noise model, the SDE is driven by a standard Wiener process.…
Breather solutions of the modified Korteweg-de Vries equation are shown to be globally stable in a natural H^2 topology. Our proof introduces a new Lyapunov functional, at the H^2 level, which allows to describe the dynamics of small…
In this paper we establish the persistence property for solutions of the quartic generalized Korteweg-de Vries equation with initial data in weighted Sobolev spaces $H^{s}(\mathbb{R})\cap L^2(|x|^{2r}dx)$ for $s =1/12 + \varepsilon$ and any…
R\"ockner and Zhang in [27] proved the existence of a unique strong solution to a stochastic tamed 3D Navier-Stokes equation in the whole space and for the periodic boundary case using a result from [31]. In the latter case, they also…
This work aims to investigate the well-posedness and the existence of ergodic invariant measures for a class of third grade fluid equations in bounded domain $D\subset\mathbb{R}^d,d=2,3,$ in the presence of a multiplicative noise. First, we…
Some textbooks and reports claim that the Jacobian which arises in the discussion of the Faddeev-Popov method to quantize non-Abelian gauge theories and which is given by the derivative of the gauge fixing conditions over the gauge group…
In this article, we study stochastic partial differential equations with two reflecting walls, driven by space-time white noise with non-constant diffusion coefficients under periodic boundary conditions. The existence and uniqueness of…
In this paper, we consider the KPZ equation driven by space-time white noise replaced with its fractional derivatives of order $\gamma>0$ in spatial variable. A well-posedness theory for the KPZ equation is established by Hairer [3] as an…
We study the transport properties of the Gaussian measures on Sobolev spaces under the dynamics of the two-dimensional defocusing cubic nonlinear wave equation (NLW). Under some regularity condition, we prove quasi-invariance of the…
We show how to apply ideas from the theory of rough paths to the analysis of low-regularity solutions to non-linear dispersive equations. Our basic example will be the one dimensional Korteweg--de Vries (KdV) equation on a periodic domain…
We explore Seiberg-like dualities, or mutations, for ${\cal N}=4$ quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed…
In this article, we study the continuity in law of the solutions of two linear multiplicative SPDEs (the parabolic Anderson model and the hyperbolic Anderson model) with respect to the spatial parameter of the noise. The solution is…
We identify the representation of the square of white noise obtained by L. Accardi, U. Franz and M. Skeide in [Comm. Math. Phys. 228 (2002), 123--150] with the Jacobi field of a L\'evy process of Meixner's type.
The paper is devoted to studying the asymptotics of the family $(\mu^\varepsilon)$ of stationary measures of the Markov process generated by the flow of stochastic 2D Navier-Stokes equation with smooth white noise. By using the large…
In this paper, we investigate the quantitative exponential stability of the Korteweg-de Vries equation on a finite interval with its length close to the critical set. Sharp decay estimates are obtained via a constructive PDE control…
By exploiting the fact that conservation laws form the kernel of a discrete Euler operator, we use a recently introduced symbolic-numeric approach to construct a new class of finite difference methods for the modified Korteweg-de Vries…
We study the long time statistics of a two-dimensional Hamiltonian system in the presence of Gaussian white noise. While the original dynamics is known to exhibit finite time explosion, we demonstrate that under the impact of the stochastic…
We investigate the global well-posedness and ergodicity of the complex Ginzburg-Landau equation with a general nonlinear term on the two-dimensional torus, driven by complex-valued space-time white noise. Due to the roughness of noise, the…