Related papers: Multidimensional potential Burgers turbulence
We construct space-time stationary solutions of the 1D Burgers equation with random forcing in the absence of periodicity or any other compactness assumptions. More precisely, for the forcing given by a homogeneous Poissonian point field in…
In this work, we consider the incompressible generalized Navier-Stokes-Voigt equations in a bounded domain $\mathcal{O}\subset\mathbb{R}^d$, $d\geq 2$, driven by a multiplicative Gaussian noise. The considered momentum equation is given by:…
We consider a damped/driven nonlinear Schr\"odinger equation in an $n$-cube $K^{n}\subset\mathbb{R}^n$, $n$ is arbitrary, under Dirichlet boundary conditions \[ u_t-\nu\Delta u+i|u|^2u=\sqrt{\nu}\eta(t,x),\quad x\in K^{n},\quad u|_{\partial…
The irreversible turbulent energy cascade epitomizes strongly non-equilibrium systems. At the level of single fluid particles, time irreversibility is revealed by the asymmetry of the rate of kinetic energy change, the Lagrangian power,…
We consider the stochastic Burgers equation $ \dnachd{t} \psi(t,r) = \Delta \psi(t,r) + \nabla \psi^2(t,r)+\sqrt{\gamma\psi(t,r)} \eta(t,r) $ with periodic boundary conditions, where $t \ge 0,$ $r \in [0,1],$ and $\eta$ is some space-time…
This paper studies the finite time explosion of the stochastic heat equation $\frac{\partial u}{\partial t}(t,x)=\frac{\partial^2}{\partial x^2} u(t,x)+(u(t,x))^{\beta}+\sigma(u(t,x))\dot{W}(t,x)$. We consider an interval $D=[-\pi,\pi]$…
We prove the global-in-time existence of weak solutions to the Navier-Stokes equations of compressible isentropic flow in three space dimensions with adiabatic exponent $\gamma\ge1$. Initial data and solutions are small in $L^2$ around a…
This paper examines the properties of a regularization of Burgers equation in one and multiple dimensions using a filtered convective velocity, which we have dubbed as convectively filtered Burgers (CFB) equation. A physical motivation…
We consider the Burgers equation on $H=L^2(0,1)$ perturbed by white noise and the corresponding transition semigroup $P_t$. We prove a new formula for $P_tD\varphi$ (where $\varphi:H\to\R$ is bounded and Borel) which depends on $\varphi$…
We construct a solution to the spatially periodic $d$-dimensional Navier-Stokes equations with a given distribution of the initial data. The solution takes values in the Sobolev space $H^\alpha$, where the index $\alpha\in R$ is fixed…
In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked…
We consider the damped hyperbolic equation in one space dimension $\epsilon u_{tt} + u_t = u_{xx} + F(u)$, where $\epsilon$ is a positive, not necessarily small parameter. We assume that $F(0)=F(1)=0$ and that $F$ is concave on the interval…
We study the Complex Ginzburg--Landau initial value problem $\partial_t u=(1+i\alpha) \partial_x^2 u + u - (1+i\beta) u |u|^2$, $u(x,0)=u_0(x)$ for a complex field $u\in{\bf C}$, with $\alpha,\beta\in{\bf R}$. We consider the Benjamin--Feir…
Extending results of Humpherys-Lyng-Zumbrun in the one-dimensional case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the multidimensional stability of planar Navier--Stokes shocks…
It is shown that the generalizations to more than one space dimension of the pole decomposition for the Burgers equation with finite viscosity and no force are of the form u = -2 viscosity grad log P, where the P's are explicitly known…
We consider the time-dependence of a hierarchy of scaled $L^{2m}$-norms $D_{m,\omega}$ and $D_{m,\theta}$ of the vorticity $\boldsymbol {\omega} = \boldsymbol{\nabla} \times {\mathbf u}$ and the density gradient $\boldsymbol{\nabla}…
The following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) with potential \begin{equation*} \frac{\partial \boldsymbol{y}}{\partial t}-\mu…
We present the $L_p$-solvability for stochastic time fractional Burgers' equations driven by multiplicative space-time white noise: $$ \partial_t^\alpha u = a^{ij}u_{x^ix^j} + b^{i}u_{x^i} + cu + \bar b^i u u_{x^i} +…
Thermodynamically consistent fractional Burgers constitutive models for viscoelastic media, divided into two classes according to model behavior in stress relaxation and creep tests near the initial time instant, are coupled with the…
We consider solutions to linear parabolic SPDEs of the form \[ \mathrm{d} u(t) + A u(t)\, \mathrm{d} t = g(t)\, \mathrm{d} \beta, \qquad u(0)=0, \] where $A$ is a positive, invertible, and self-adjoint operator on a Hilbert space $X$,…