Related papers: Singularities in one-dimensional Euler flows
The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analysed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and…
The dynamics of self-gravitating fluid bodies is described by the Euler-Einstein system of partial differential equations. The break-down of well-posedness on the fluid-vacuum interface remains a challenging open problem, which is…
The development of the classical physics fundamentals with usage of experience of the experimental and computational-analytical investigations has allowed to create the valid conception of a fluid motion. The multidisciplinary approach on a…
We review recent advances in understanding singularity and small scales formation in solutions of fluid dynamics equations. The focus is on the Euler and surface quasi-geostrophic (SQG) equations and associated models.
The aim of this paper is to study a system of three equations for ionized gas dynamics at high temperature, in one spatial dimension. In addition to the mass density, pressure and particle velocity, a further quantity is needed, namely, the…
Invariants at arbitrary and fixed energy (strongly and weakly conserved quantities) for 2-dimensional Hamiltonian systems are treated in a unified way. This is achieved by utilizing the Jacobi metric geometrization of the dynamics. Using…
In this paper we developed an analysis of the compressible, isentropic Euler equations in two spatial dimensions for a generalized polytropic gas law. The main focus is rotational flows in the subsonic regimes, described through the…
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…
On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the…
We investigate the vacuum in nonisentropic gas dynamics in one space variable, with the most general equation of states allowed by thermodynamics. We recall physical constraints on the equations of state and give explicit and easily…
We study the formation of singularity for the Euler-Poisson system equipped with the Boltzmann relation, which describes the dynamics of ions in an electrostatic plasma. In general, it is known that smooth solutions to nonlinear hyperbolic…
Lie point symmetries of the one-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates are considered. Complete Lie group classification of these equations reduced to a scalar second-order PDE is performed. The…
We study a nonlinear wave for a system of balance laws in one space dimension, which describes combustion for two-phase (gas and liquid) flow in porous medium. The problem is formulated for a general $N$-component liquid for modeling the…
We study steady-state properties of inelastic gases in two-dimensions in the presence of an energy source. We generalize previous hydrodynamic treatments to situations where high and low density regions coexist. The theoretical predictions…
This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and…
We consider the two dimensional unsteady Prandtl system. For a special class of outer Euler flows and solutions of the Prandtl system, the trace of the tangential derivative of the tangential velocity along the transversal axis solves a…
We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations…
This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which…
We propose a generalization of equations of quantum mechanics in the hydrodynamic form by introducing the terms taking into account the diffusion velocity at zero and finite temperatures and the density energy of diffusion pressure of the…
The Lagrangian fluid description is employed to solve the initial value problem for one-dimensional, compressible fluid flows represented by the Euler-Poisson system. Exact nonlinear and time-dependent solutions are obtained, which exhibit…