相关论文: Time-delayed instabilities in complex Burgers equa…

The large-time behavior of solutions to Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context…

The numerical simulation of the inviscid Burgers' equation is often hindered by spurious oscillations near discontinuities. To mitigate this issue, a viscous term can be introduced, leading to the viscous Burgers' equation. In this work,…

We consider the large time behavior of strong solutions to a kind of stochastic Burgers equation, where the position x is perturbed by a Brownian noise. It is well known that both the rarefaction wave and viscous shock wave are…

We investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, we quantify the divergence of initially…

We investigate large time existence of solutions of the Navier-Stokes-Boussinesq equations with spatially almost periodic large data when the density stratification is sufficiently large. In 1996, Kimura and Herring \cite{KH} examined…

We consider the non-homogeneous generalised Burgers equation \frac{\partial u}{\partial t} + f'(u)\frac{\partial u}{\partial x} - \nu \frac{\partial^2 u}{\partial x^2} = \eta,\ t \geq 0,\ x \in S^1. Here f is strongly convex and satisfies a…

Burgers turbulence supported by white-in-time random forcing at low wavenumbers is studied analytically and by computer simulation. It is concluded that the probability density Q of velocity gradient displays four asymptotic regimes at very…

In this work, high order splitting methods have been used for calculating the numerical solutions of the Burgers' equation in one space dimension with periodic and Dirichlet boundary conditions. However, splitting methods with real…

We use the mapping between Burgers' equation and the problem of a directed polymer in a random medium in order to study the fully developped turbulence in the $N$ dimensional forced Burgers' equation. The stirring force corresponds to a…

Simulations of elastic turbulence, the chaotic flow of highly elastic and inertialess polymer solutions, are plagued by numerical difficulties: The chaotically advected polymer conformation tensor develops extremely large gradients and can…

This work is devoted to investigating stochastic turbulence for the fluid flow in one-dimensional viscous Burgers equation perturbed by L\'evy space-time white noise with the periodic boundary condition. We rigorously discuss the regularity…

For the Burgers equation driven by thermal noise leading asymptotics of pair and high-order correlators of the velocity field are found for finite times and large distances. It is shown that the intermittency takes place: some correlators…

Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…

Origin of hydrodynamical instability and turbulence in the Keplerian accretion disc as well as similar laboratory shear flows, e.g. plane Couette flow, is a long standing puzzle. These flows are linearly stable. Here we explore the…

We performed molecular dynamics simulations to investigate the clustering instability of a freely cooling dilute gas of inelastically colliding disks in a quasi-one-dimensional setting. We observe that, as the gas cools, the shear stress…

For some deterministic nonlinear PDEs on the torus whose solutions may blow up in finite time, we show that, under suitable conditions on the nonlinear term, the blow-up is delayed by multiplicative noise of transport type in a certain…

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 prove that the stochastic Burgers equation on $\mathbf{R}^{d}$, $d<4$, forced by gradient noise that is white in time and smooth in space, admits spacetime-stationary solutions. These solutions are thus the gradients of solutions to the…

We study the equations obtained from linearizing the compressible Navier-Stokes equations around a steady-state profile with a heavier fluid lying above a lighter fluid along a planar interface, i.e. a Rayleigh-Taylor instability. We…

In his first 1941 paper Kolmogorov assumed that the velocity has increments which are homogeneous and independent of the velocity at a suitable reference point. This assumption of local homogeneity is consistent with the nonlinear dynamics…