Related papers: Stabilities for Euler-Poisson Equations in Some Sp…
The main concern of this paper is to study large-time behavior of the sheath to the full Euler-Poisson system. As is well known, the monotone stationary solution under the Bohm criterion can be referred to as the sheath which is formed by…
In this paper we perform stability analysis for exponential solutions in Einstein-Gauss-Bonnet and cubic Lovelock gravity. We report our findings, provide areas on parameters space and discuss familiarities and differences between cases.…
About thirty years ago we looked for "minimal assumptions" on the data which guarantee that solutions to the $\,2-D\,$ evolution Euler equations in a bounded domain are classical. Classical means here that all the derivatives appearing in…
This paper investigates rotating star solutions to the Euler-Poisson equations with a non-isentropic equation of state. As a first step, the equation for gas density with a prescribed entropy and angular velocity distribution is studied.…
The Navier-Stokes motions in cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions are proved. The solutions are bounded by the same constant for all time.…
The global well-posedness and stability of solutions to the three-dimensional compressible Euler equations with damping is a longstanding open problem. This problem was addressed in \cite{WY, STW} in the isentropic regime (i.e. $\gamma>1$)…
A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether's Theorem to determine conservation laws for the field equations. In the…
We study the Euler-Poincar\'e equations that are the regularized Euler equations derived from the Euler-Poincar\'e framework. It is noteworthy to remark that the Euler-Poincar\'e equations are a generalization of two well-known…
The time evolution of a two-component collisionless plasma is modeled by the Vlasov-Poisson system. In this work, the setting is two and one-half dimensional, that is, the distribution functions of the particles species are independent of…
We prove a sharp orbital stability result for a class of exact steady solutions, expressed in terms of Bessel functions of the first kind, of the two-dimensional incompressible Euler equation in a disk. A special case of these solutions is…
We prove the linear and nonlinear asymptotic stability of small amplitude one-dimensional solitary waves submitted to small localized irrotational perturbations in the three dimensional Euler-Poisson system describing the dynamics of ions.…
In this paper, we prove the existence of two-dimensional solutions to the steady Euler-Poisson system with continuous transonic transitions across sonic interfaces of codimension 1. First, we establish the well-posedness of a boundary value…
In this paper we perform systematic investigation of all possible solutions with static compact extra dimensions and expanding three-dimensional subspace (``our Universe''). Unlike previous papers, we consider extra-dimensional subspace to…
We study some aspects of dynamical compactification scenario where stabilisation of extra dimensions occurs due to presence the Gauss-Bonnet term and non-zero spatial curvature. In the framework of the model under consideration there exists…
Goldreich-Weber solutions constitute a finite-parameter of expanding and collapsing solutions to the mass-critical Euler-Poisson system. Two subclasses of this family correspond to compactly supported density profiles suitably modulated by…
We prove nonlinear stability of the Larson-Penston family of self-similarly collapsing solutions to the isothermal Euler-Poisson system. Our result applies to radially symmetric perturbations and it is the first full nonlinear stability…
We consider a special class of infinite energy solutions to the inviscid incompressible porous medium equations (IPM), introduced in Castro-C\'ordoba-Gancedo-Orive [9]. The (IPM) equations then reduce to a one-dimensional nonlocal nonlinear…
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…
The linearized operator for non-radial oscillations of spherically symmetric self-gravitating gaseous stars is analyzed in view of the functional analysis. The evolution of the star is supposed to be governed by the Euler-Poisson equations…
We are interested in the stability analysis of two-dimensional incompressible inviscid fluids. Specifically, we revisit a recent result on the stability of Yudovich's solutions to the incompressible Euler equations in $L^\infty([0,T];H^1)$…