相关论文: Shock Formation of 3D Euler-Poisson System for Ele…
This paper concerns with the existence of transonic shocks for steady Euler flows in a 3-D axisymmetric cylindrical nozzle, which are governed by the Euler equations with the slip boundary condition on the wall of the nozzle and a receiver…
The collision of two plasma clouds at a speed that exceeds the ion acoustic speed can result in the formation of shocks. This phenomenon is observed not only in astrophysical scenarios such as the propagation of supernova remnant (SNR)…
We prove finite time blowup of the Burgers-Hilbert equation. We construct smooth initial data with finite $H^5$-norm such that the $L^\infty$-norm of the spacial derivative of the solution blows up. The blowup is an asymptotic self-similar…
Electrons in an expanding ultracold plasma are expected to be in quasi-equilibrium, since the collision times are short compared to the plasma lifetime, yet we observe electrons evaporating out as the ion density decreases during expansion.…
We present an analytical model for electron self-injection in nonlinear, multidimensional plasma wave excited by short laser pulse in the bubble regime or by short electron beam in the blowout regime. In this regimes, which are typical for…
We study the singularity formation of smooth solutions of the relativistic Euler equations in $(3+1)$-dimensional spacetime for both finite initial energy and infinite initial energy. For the finite initial energy case, we prove that any…
In recent work we have developed a renormalization framework for stabilizing reduced order models for time-dependent partial differential equations. We have applied this framework to the open problem of finite-time singularity formation…
Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this paper, we present some new numerical evidence that the 3D…
The manuscript reports the observation of time dependent localized and non-propagating structures in the coupled laser plasma system through 1-D fluid and PIC simulations. It is reported that such structures form spontaneously as a result…
In this work, we examine sheath formation in the presence of bias potentials in the current saturation regime for pulsed power fusion experiments. It is important to understand how the particle and heat fluxes at the wall may impact the…
From an open set of initial data, we construct a family of classical solutions to the 1D nonisentropic compressible Euler equations which form $C^{0,\nu}$ cusps as a first singularity, for any $\nu \in [1/2,1)$. For this range of $\nu$,…
The formation of a singularity in a compressible gas, as described by the Euler equation, is characterized by the steepening, and eventual overturning of a wave. Using a self-similar description in two space dimensions, we show that the…
The study presented in this paper has shown that the generation of hard x rays and high-energy ions, which are detected in pinch implosion experiments, may be associated with the Coulomb explosion of the hot spot that is formed due to the…
The formation of collisionless shock fronts is an ubiquitous phenomenon in space plasma environments. In the solar wind shocks might accompany coronal mass ejections, while even more violent events, such as supernovae, produce shock fronts…
Three dimensional (3D) relativistic electromagnetic sub-cycle solitons were observed in 3D Particle-in-Cell simulations of an intense short laser pulse propagation in an underdense plasma. Their structure resembles that of an oscillating…
The three-dimensional incompressible Boussinesq system is one of the important equations in fluid dynamics. The system describes the motion of temperature-dependent incompressible flows. And the temperature naturally has diffusion.…
In his 2007 monograph, D. Christodoulou proved a breakthrough result giving a detailed description of the formation of shocks in solutions to the relativistic Euler equations in three spatial dimensions. He assumed that the data have small…
We study in this article the blow-up of solutions to a coupled semilinear wave equations which are characterized by linear damping terms in the \textit{scale-invariant regime}, time-derivative nonlinearities, mass terms and Tricomi terms.…
The Euler-Poisson (EP) system describes the dynamic behavior of many important physical flows. In this work, a Riccati system that governs two-dimensional EP equations is studied. The evolution of divergence is governed by the Riccati type…
Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out…