Related papers: Eulerian dynamics in multi-dimensions with radial …
We consider a new variant of cosmological perturbation theory that has been designed specifically to include non-linear density contrasts on scales 100 Mpc, while still allowing for linear fluctuations on larger scales. This theory is used…
We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form with a combination of acoustic and Dirichlet boundary…
We study the nonexistence of multi-dimensional solitary waves for the Euler-Poisson system governing ion dynamics. It is well-known that the one-dimensional Euler-Poisson system has solitary waves that travel faster than the ion-sound…
We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the…
In this paper, we present a novel Eulerian-Lagrangian formulation for the compressible isentropic Euler equations with vaccum. Using the developed Lagrangian flow map formulation, we show a short-time solution for a general pressure law. A…
We introduce a variational time discretization for the multi-dimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each timestep requires the minimization of a functional measuring the…
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…
Hodograph equations for the n-dimensional Euler equations with the constant pressure and external force linear in velocity are presented. They provide us with solutions of the Euler in implicit form and information on existence or absence…
We study the large-time asymptotic behavior of solutions to the one-dimensional damped pressureless Euler-Poisson system with variable background states, subject to a neutrality condition. In the case where the background density converges…
We investigate the non-equilibrium dynamics of a class of isolated one-dimensional systems possessing two degenerate ground states, initialized in a low-energy symmetric phase. We report the emergence of a time-scale separation between fast…
We analyse the one-dimensional pressureless Euler-Poisson equations with a linear damping and non-local interaction forces. These equations are relevant for modelling collective behavior in mathematical biology. We provide a sharp threshold…
We consider global-in-time evolution of irrotational, isentropic, compressible Euler flow in $3$-D, for a broad class of $H^4$ classical Cauchy data without assuming symmetry, prescribed on an annulus surrounded by a constant state in the…
This paper contributes to the study of large data problems for $C^1$ solutions of the relativistic Euler equations. In the $(1+1)$-dimensional spacetime setting, if the initial data are away from vacuum, a key difficulty in proving the…
We show that the question about the criterion of a singularity formation for radially symmetric solutions to the Cauchy problem for a fairly wide class of equations related to the pressureless Euler-Poisson equations can be reduced to the…
We present a preliminary study of a new phenomena associated with the Euler-Poisson equations -- the so called critical threshold phenomena, where the answer to questions of global smoothness vs. finite time breakdown depends on whether the…
We construct a new class of self-similar implosion profiles for the multi-dimensional compressible Euler equations. These profiles are smooth, genuinely non-isentropic, radially/spherically symmetric, and have explicit (closed-form)…
A new framework based on Boltzmann equation which is genuinely multidimensional and mesh-less is developed for solving Euler's equations. The idea is to use the method of moment of Boltzmann equation to operate in multidimensions using…
Eulerian hydrodynamical simulations are a powerful and popular tool for modeling fluids in astrophysical systems. In this work, we critically examine recent claims that these methods violate Galilean invariance of the Euler equations. We…
A good generalization of the Euclidean dimension to disordered systems and non crystalline structures is commonly required to be related to large scale geometry and it is expected to be independent of local geometrical modifications. The…
We study various formulations of the boundary conditions for the Euler equations of gas dynamics from a mathematical and numerical point of view. In the case of one space dimension, we recall the classical results, based on an analysis of…