Related papers: Taub, Rindler, and the static plate
We study stationary homogeneous solutions to the 3D Euler equation. The problem is motivated be recent exclusions of self-similar blowup for Euler and its relation to Onsager conjecture and intermittency. We reveal several new classes of…
We study the convergence rate of the solutions of the incompressible Euler-$\alpha$, an inviscid second-grade complex fluid, equations to the corresponding solutions of the Euler equations, as the regularization parameter $\alpha$…
A class of stationary rigidly rotating perfect fluid coupled with non-linear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found, for the equation of state…
This paper investigates the extendability of local solutions for incompressible 3D Navier-Stokes and 3D Euler problems, with initial data $\mathbf{u}_0$ in the Sobolev space $H^s (\mathbb{R}^3)$, where $s$ ensures the existence and…
The motion of a rigid body immersed in an incompressible perfect fluid which occupies a three- dimensional bounded domain have been recently studied under its PDE formulation. In particular classical solutions have been shown to exist…
In the framework of Einstein's the theory of general relativity we present a new interior solution with a perfect fluid, this is constructed from the proposal of a gravitational redshift factor. The geometry is regular and its density and…
We consider the relativistic Euler equations governing spherically symmetric, perfect fluid flows on the outer domain of communication of Schwarzschild spacetime, and we introduce a version of the finite volume method which is formulated…
We give a geometric formulation of 3D incompressible Euler that contains the Eulerian and Lagrangian gauges as special cases. In the Lagrangian gauge, incompressible Euler is a real analytic ODE in Banach space; a short proof of this known…
We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely…
The properties of some locally rotationally symmetric (LRS) perfect fluid space-times are examined in order to demonstrate the usage of the description of geometries in terms of the Riemann tensor and a finite number of its covariant…
In this work we study static perfect fluid stars in 2+1 dimensions with an exterior BTZ spacetime. We found the general expression for the metric coefficients as a function of the density and pressure of the fluid. We found the conditions…
We consider solutions of the Einstein equations with cosmological constant $\Lambda\neq 0$ admitting conformal compactification with smooth scri $\mathscr{I^+}$. Metrics are written in the Bondi-Sachs coordinates and expanded into inverse…
Indefinite Kaehler solutions of the Einstein equations are studied, and it is almost completely determined which compact complex surfaces admit such metrics.
The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled…
Building upon the pioneering work [Merle, Rapha\"el, Rodnianski, and Szeftel, Ann. of Math., 196(2):567-778, 2022, Ann. of Math., 196(2):779-889, 2022, Invent. Math., 227(1):247-413, 2022] we construct exact, smooth self-similar imploding…
Solutions to Einstein's vacuum equations in three dimensions are locally maximally symmetric. They are distinguished by their global properties and their investigation often requires a choice of gauge. Although analyses of this sort have…
We present a novel homogeneous and geometrically flat exact solution of Einstein's General Relativity equations for an ideal fluid. The solution, which describes an expanding/contracting hypercylinder, fits well with the observational…
We investigate the interior Einstein's equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational…
We ask the following question: Of the exact solutions to Einstein's equations extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The candidate…
The exact global solution of the Einstein equations [Neugebauer & Meinel, Phys. Rev. Lett. 75 (1995) 3046] describing a rigidly rotating, self-gravitating disk is discussed. The underlying matter model is a perfect fluid in the limit of…