相关论文: Shock Formation of 3D Euler-Poisson System for Ele…
Spherical or cylindrical convergent shock waves in imploding materials are one of the most effective ways to produce extremely high pressures, densities and temperatures, hardly attainable in plane shock waves generated by chemical high…
It is shown that collisionless shock waves can be driven in unmagnetized electron-positron plasmas by performing a two-dimensional particle-in-cell simulation. At the shock transition region, strong magnetic fields are generated by a…
The evolution of a pair of point vortices in whole space, subject to the inviscid Euler equations for incompressible fluid flow, is solved exactly for rotationally symmetric initial conditions. This exact solution shows that the vortex…
We consider a one-parameter family of 1D models for the 3D axisymmetric incompressible Euler equation with $C^{\alpha}$ vorticity and without swirl near the symmetry axis. For $\alpha = \frac13$, we impose a crucial normalization and…
In this work, a one-dimensional simulation code was developed for both single-phase and two-phase systems, focusing on time-dependent Euler equations for gas and particles. These equations, non-linear hyperbolic conservation laws, describe…
We solve the equations of radiation hydrodynamics in the two-temperature fluid approximation on an adaptive grid. The temperature structure depends upon the electron-ion energy exchange length, $l_{ei}$, and the electron conduction length,…
We investigate rescaling transformations for the Vlasov-Poisson and Euler-Poisson systems and derive in the plasma physics case Lyapunov functionals which can be used to analyze dispersion effects. The method is also used for studying the…
Electrostatic two-stream instabilities play essential roles in an electrostatic collisionless shock formation. They are a key dissipation mechanism and result in ion heating and acceleration. Since the number and energy of the…
We construct a new class of asymptotically self-similar finite-time blowups that have two collapsing spatial scales for the 1D Constantin-Lax-Majda model. The larger spatial scale measures the decreasing distance between the bulk of the…
In the paper [Li Jun, Xu Gang, Yin Huicheng, On the blowup mechanism of smooth solutions to 1D quasilinear strictly hyperbolic systems with large variational initial data, Nonlinearity 38 (2025), No.2, 025016], for the 1-D $n\times n$…
The dispute on whether the three-dimensional (3D) incompressible Euler equations develop an infinitely large vorticity in a finite time (blowup) keeps increasing due to ambiguous results from state-of-the-art direct numerical simulations…
We review and apply the continuous symmetry approach to find the solution of the 3D Euler fluid equations in several instances of interest, via the construction of constants of motion and infinitesimal symmetries, without recourse to…
The Euler-Maxwell system describes the evolution of a plasma when the collisions are important enough that each species is in a hydrodynamic equilibrium. In this paper we prove global existence of small solutions to this system set in the…
Fluid simulations, which are considerably simpler and faster, have been employed to study the behavior of the wakefield driven by a relativistic rigid beam in a 2-D cold plasma. When the transverse dimensions of the beam are chosen to be…
We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an…
In this paper we continue to study the shock formation for the $3$-dimensional quasilinear wave equation \begin{align}\label{main eq} -(1+3G"(0)(\partial_{t}\phi)^{2})\partial^{2}_{t}\phi+\Delta\phi=0,\tag{\textbf{$\star$}} \end{align} with…
Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation.…
The one-dimensional flight of a fast electron flux in plasma is investigated taking into account generation and absorption of plasma waves. The transition from the kinetic description to the gas dynamics is made. The closed set of gas…
We demonstrate a novel setup for hybrid particle-in-cell simulations designed to isolate the physics of the shock precursor over long time periods for significantly lower computational cost than previous methods. This is achieved using a…
We present the first demonstration of finite-time gradient blow-ups in Israel-Stewart (IS) theories with 1+1D plane symmetry, mathematically showing the existence of smooth initial data that can evolve into shocks across three regimes: pure…