相关论文: The Gaussian Structure of the Singular Stochastic …
In this paper, we study the well-posedness of Fractional Rough Burgers equation driven by space-time noise in $H^s(\mathbb T)$ space. For the higher dissipation $\gamma\in(\frac{4}{3},2]$, we establish local well-posedness. Global…
Motivated by the regularization by noise phenomenon for SDEs we prove existence and uniqueness of the flow of solutions for the non-Lipschitz stochastic heat equation $$\frac{\partial u}{\partial t}=\frac12\frac{\partial^2 u}{\partial z^2}…
We study the statistical properties of solutions to Burgers' equation, $v_t + vv_x = \nu v_{xx}$, for large times, when the initial velocity and its potential are stationary Gaussian processes. The initial power spectral density at small…
Our understanding of the one-dimensional KPZ equation, \textit{alias} noisy Burgers equation, has advanced substantially over the past five years. We provide a non-technical review, where we limit ourselves to the stochastic PDE and lattice…
When a gas of particles interacts with much a larger reservoir the density dynamics on large scales is typically governed by diffusion. We study this paradigmatic problem for weakly coupled integrable systems and show that this picture gets…
We prove the existence of a sticky-reflected solution to the heat equation on the spatial interval $[0,1]$ driven by colored noise. The process can be interpreted as an infinite-dimensional analog of the sticky-reflected Brownian motion on…
We carry out enhanced symmetry analysis of a two-dimensional Burgers system. The complete point symmetry group of this system is found using an enhanced version of the algebraic method. Lie reductions of the Burgers system are…
We show that for a given holomorphic noncharacteristic surface S in two-dimensional complex space, and a given holomorphic function on S, there exists a unique meromorphic solution of Burgers' equation which blows up on S. This proves the…
We are interested in the life span and the asymptotic behaviour of the solutions to a system governing the motion of a pressureless gas, submitted to a strong, inhomogeneous magnetic field $ \e^{-1} B(x)$, of variable amplitude but fixed…
In this paper, we establish the existence and uniqueness of solutions to the two-dimensional Burgers equation using the framework of infinite-dimensional dynamical systems. The two-dimensional Burgers equation, which models the interplay…
We study a generalized 1d periodic SPDE of Burgers type: $$ \partial_t u =- A^\theta u + \partial_x u^2 + A^{\theta/2} \xi $$ where $\theta > 1/2$, $-A$ is the 1d Laplacian, $\xi$ is a space-time white noise and the initial condition $u_0$…
In this work, we use the spectral Galerkin method to prove the existence of a pathwise unique mild solution of a fractional stochastic partial differential equation of Burgers type in a H\"older space. We get the temporal regularity and…
This paper proves the existence of unstable shocks of the Burgers-Hilbert equation conjectured in arXiv:2006.05568. More precisely, we construct smooth initial data with finite $H^9$-norm such that the solution in self-similar coordinates…
A nondispersive, conservative regularisation of the inviscid Burgers equation is proposed and studied. Inspired by a related regularisation of the shallow water system recently introduced by Clamond and Dutykh, the new regularisation…
In this paper, we explore a nonlocal inviscid Burgers equation. Fixing a parameter $h$, we prove existence and uniqueness of the local solution of the equation $\InviscidBurgersNonlocal{u}$ with periodic initial condition. We also explore…
We consider the one-dimensional stochastic heat and wave equations driven by Gaussian noises with constant initial conditions. We study the spatial average of the solutions on an interval of length $R$ and show that the family of laws of…
We present a complete analytical resolution of the one dimensional Burgers equation with the elastic forcing term $-\kappa^{2} x+f(t)$, $\kappa\in\mathbb{R}$. Two methods existing for the case $\kappa=0$ are adapted and generalized using…
The asymptotic solution of the inviscid Burgers equations with initial potential $\psi$ is closely related to the convex hull of the graph of $\psi$. In this paper, we study this convex hull, and more precisely its extremal points, if…
We consider a stochastic conservation law on the line with solution-dependent diffusivity, a super-linear, sub-quadratic Hamiltonian, and smooth, spatially-homogeneous kick-type random forcing. We show that this Markov process admits a…
The shock discontinuities, generically present in inviscid solutions of the forced Burgers equation, and their bifurcations happening in the course of time (perestroikas) are classified in two and three dimensions -- the one-dimensional…