相关论文: A sparse resolution of the DiPerna-Majda gap probl…

This paper is devoted to show a couple of typicality results for weak solutions $v\in C^\theta$ of the Euler equations, in the case $\theta<1/3$. It is known that convex integration schemes produce wild weak solutions that exhibit anomalous…

In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…

This paper proposes a new general methodology for finite-time singularity formation for moving interface problems involving the incompressible Euler equations in the plane. The first problem considered is the two-phase Euler vortex sheets…

In this paper, we are concerned with the asymptotic behavior of solutions of M1 model proposed in the radiative transfer fields. Starting from this model, combined with the compressible Euler equation with damping, we introduce a more…

We investigate solutions of the 2d incompressible Euler equations, linearized around steady states which are radially decreasing vortices. Our main goal is to understand the smoothness of what we call the spectral density function…

A basic example of shear flow was introduced by DiPerna and Majda to study the weak limit of oscillatory solutions of the Euler equations of incompressible ideal fluids. In particular, they proved by means of this example that weak limit of…

The second-grade fluid equations are a model for viscoelastic fluids, with two parameters: $\alpha > 0$, corresponding to the elastic response, and $\nu > 0$, corresponding to viscosity. Formally setting these parameters to $0$ reduces the…

The concept of renormalized dissipative measures-valued (rDMV) solutions to a complete Euler system for a perfect gas was introduced in [8] and further discussed in [9]. Moreover it was shown there that rDMV solutions satisfy the weak…

Accurate prediction of a dense spray using an Euler-Lagrange approach is challenging because of high volume fraction of the dispersed phase due to subgrid cluster of droplets. To accurately model dense sprays, one needs to capture this…

Assume that $$ Au=f,\quad (1) $$ is a solvable linear equation in a Hilbert space, $||A||<\infty$, and $R(A)$ is not closed, so problem (1) is ill-posed. Here $R(A)$ is the range of the linear operator $A$. A DSM (dynamical systems method)…

This paper is concerned with the large-time behavior of solutions to the Cauchy problem on the two-fluid Euler-Maxwell system with collisions when initial data are around a constant equilibrium state. The main goal is the rigorous…

Coherent vortices are often observed to persist for long times in turbulent 2D flows even at very high Reynolds numbers and are observed in experiments and computer simulations to potentially be asymptotically stable in a weak sense for the…

A key characteristic of the anomalous sub-solution equation is that the solution exhibits algebraic decay rate over long time intervals, which is often refered to the Mittag-Leffler type stability. For a class of power nonlinear…

The one-dimensional PDE model of the wave equation with a state feedback controller at its boundary, which describes wave dynamics of a wide-range of controlled mechanical systems, has exponentially stable solutions. However, it is known…

In this article we consider weak solutions of the Euler-$\alpha$ equations in the full plane. We take, as initial unfiltered vorticity, an arbitrary nonnegative, compactly supported, bounded Radon measure. Global well-posedness for the…

The goal of this numerical study is to get insight into singular solutions of the two-dimensional (2D) Euler equations for non-smooth initial data, in particular for vortex sheets. To this end high resolution computations of vortex layers…

We study a finite-element based space-time discretisation for the 2D stochastic Navier-Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal convergence rates in the energy norm with respect to…

A singularly perturbed reaction-diffusion problem posed on the unit square in $\mathbb{R}^2$ is solved numerically by a local discontinuous Galerkin (LDG) finite element method. Typical solutions of this class of 2D problems exhibit…

In this paper we study jump-diffusion stochastic differential equations (SDEs) with a discontinuous drift coefficient and a possibly degenerate diffusion coefficient. Such SDEs appear in applications such as optimal control problems in…

We study a finite form of the classical interval discrepancy problem. Starting from the unit interval, one repeatedly splits an existing interval into two until $n$ intervals have been produced. The discrepancy of such a process is the…