相关论文: Damped Euler system with attractive Riesz interact…
The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time external forces all two dimensional regular solutions converge to…
The collective behavior of animals can be modeled by a system of equations of continuum mechanics endowed with extra terms describing repulsive and attractive forces between the individuals. This system can be viewed as a generalization of…
We investigate the Cauchy problem for the Vlasov--Riesz system, which is a Vlasov equation featuring an interaction potential generalizing previously studied cases, including the Coulomb $\Phi = (-\Delta)^{-1}\rho$, Manev $(-\Delta)^{-1} +…
We study the long-time behavior of solutions to the compressible Euler equations with frictional damping in the whole space, where we prescribe direction-dependent values for the density at spatial infinity. To this end, we transform the…
In mathematical physics, the pressure function is determined by the equation of state. There are two existing barotropic state equations: the state equation for polytropic gas with adiabatic index greater than or equal to 1 and the state…
We study the one-dimensional isentropic compressible Euler equations with linear (frictional) damping, subject to multiplicative, white-in-time stochastic forcing. The system is posed on a bounded interval with $L^\infty$ initial data and…
In this paper, we are concerned with the asymptotic behavior of solutions of M1 model on quadrant. From this model, combined with damped compressible Euler equations, a more general system is introduced. We show that the solutions to the…
For the incompressible and the isentropic compressible Euler equations in arbitrary space dimension, we establish the principle of localised relative energy, thus generalising the well-known relative energy method. To this end, we adapt…
We consider the Euler system describing the motion of a compressible fluid driven by a multiplicative white noise. We identify a large class of initial data for which the problem is ill posed - there exist infinitely many global in time…
We are concerned with the global existence and large time behavior of entropy solutions to the one dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations in a bounded interval. In this paper, we…
Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
In this paper, the compressible Euler system with velocity alignment and damping is considered, where the influence matrix of velocity alignment is not positive definite. Sound speed is used to reformulate the system into symmetric…
We consider damped and forced discrete nonlinear Schr\"odinger equations on the lattice $\mathbb{Z}$. First we establish the existence of periodic and quasiperiodic breather solutions for periodic and quasiperiodic driving, respectively.…
We study the mathematical properties of time-dependent flows of incompressible fluids that respond as an Euler fluid until the modulus of the symmetric part of the velocity gradient exceeds a certain, a-priori given but arbitrarily large,…
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…
We revisit a family of infinite-energy solutions of the 3D incompressible Euler equations proposed by Gibbon et al. [9] and shown to blowup in finite time by Constantin [6]. By adding a damping term to the momentum equation we examine how…
An asymptotic preserving and energy stable scheme for the barotropic Euler system under the low Mach number scaling is designed and analysed. A velocity shift proportional to the pressure gradient is introduced in the convective fluxes,…
This work explores the global existence and scattering behavior of solutions to a damped, inhomogeneous nonlinear Schrodinger equation featuring a time-dependent damping term, an inverse-square potential, and an inhomogeneous nonlinearity.…
We consider the Cauchy problem for the barotropic Euler system coupled to a vector Schr\"{o}dinger equation in the whole space. Assuming that the initial density and vector potential are small enough, and that the initial velocity is close…
We study the critical thresholds for the compressible pressureless Euler equations with pairwise attractive or repulsive interaction forces and non-local alignment forces in velocity in one dimension. We provide a complete description for…