Related papers: Burgers equation in the adhesion model
We study the one-dimensional Burgers equation in the inviscid limit for Brownian initial velocity (i.e. the initial velocity is a two-sided Brownian motion that starts from the origin x=0). We obtain the one-point distribution of the…
The well-posedness of the three space dimensional Prandtl equations is studied under some constraint on its flow structure. It reveals that the classical Burgers equation plays an important role in determining this type of flow with special…
We obtain a sharp limit H\"older continuity of the solution for the transport equations thanks to a vanishing viscosity analysis. We also derive the same control for parabolic equations and for inviscid Burgers' equation. Eventually, under…
This article is devoted to the study of the existence and uniqueness of mild solution to time- and space-fractional stochastic Burgers equation perturbed by multiplicative white noise. The required results are obtained by stochastic…
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…
This work introduces a pathwise notion of solution for the stochastic Burgers equation, in particular, our approach encompasses the Cole-Hopf solution. The developments are based on regularization arguments from the theory of distributions.
In this article we find the solution of the Burger equation with viscosity applying the boundary layer theory. In addition, we will observe that the solution of Burger equation with viscosity converge to the solution of Burger stationary…
Gathering together some existing results, we show that the solutions to the one-dimensional Burgers equation converge for long times towards the stationary solutions to the steady Burgers equation, whose Fourier spectrum is not integrable.…
We investigate non-perturbative results of inviscid forced Burgers equation supplemented to continuity equation in three-dimensions. The exact two-point correlation function of density is calculated in three-dimensions. The two-point…
We obtain precise large time asymptotics for the Cauchy problem for Burgers type equations satisfying shock profile condition. The proofs are based on the exact a priori estimates for (local) solutions of these equations and a recent result…
We study the inviscid Burgers equation on the circle $\mathbb{T}:=\mathbb{R}/\mathbb{Z}$ forced by the derivative of a Poisson point process on $\mathbb{R}\times\mathbb{T}$. We construct global solutions with mean $\theta$ simultaneously…
The generally held view that a model of large-scale structure, formed by collisionless matter in the Universe, can be based on the matter model ``dust'' fails in the presence of multi-stream flow, i.e., velocity dispersion. We argue that…
In this review we discuss the weak KPZ universality conjecture for a class of 1-d systems whose dynamics conserves one or more quantities. As a prototype example for the former case, we will focus on weakly asymmetric simple exclusion…
Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with…
The Cauchy problem for a scalar conservation laws admits a unique entropy solution when the data $u_0$ is a bounded measurable function (Kruzhkov). The semi-group $(S_t)_{t\ge0}$ is contracting in the $L^1$-distance. For the…
For the one dimensional Burgers equation with a random and periodic forcing, it is well-known that there exists a family of invariant measures, each corresponding to a different average velocity. In this paper, we consider the coupled…
We develop a new method to uniquely solve a large class of heat equations, so-called Kolmogorov equations in infinitely many variables. The equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper…
We revisit the one-dimensional Burgers equation in the inviscid limit for white-noise initial velocity. We derive the probability distributions of velocity and Lagrangian increments, measured on intervals of any length $x$. This also gives…
We study turbulence in the one-dimensional Burgers equation with a white-in-time, Gaussian random force that has a Fourier-space spectrum $\sim 1/k$, where $k$ is the wave number. From very-high-resolution numerical simulations, in the…
We explore a connection of the forced Burgers equation with the Schr\"{o}dinger (diffusive) interpolating dynamics in the presence of deterministic external forces. This entails an exploration of the consistency conditions that allow to…