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Starting from the linear sigma model with constituent quarks we derive the chiral fluid dynamics where hydrodynamic equations for the quark fluid are coupled to the equation of motion for the order-parameter field. In a static system at…

Oscillatory zoning, i.e. self-formation of spatial quasi-periodic oscillations in the composition of solid growing from aqueous solution, is analyzed theoretically. Keeping in mind systems like (Ba,Sr)SO4 we propose a 1D model that takes…

A comprehensive analysis of general relativistic spacetimes which admit a shear-free, irrotational and geodesic timelike congruence is presented. The equations governing the models for a general energy-momentum tensor are written down.…

This article is devoted to questions concerning the existence of solutions for partial differential equation problems modeling granular flows. The models studied take into account the complex threshold rheology of these flows, as well as…

We consider rotating equilibrium states of fluid deformable surfaces. These states are characterized by a force balance between centrifugal and bending forces, involve surface Killing vector fields and are independent on the surface…

We consider a two-dimensional, pure capillary drop of nearly-circular shape, having constant vorticity. We write the Craig-Sulem equations on the unit circle, then on the flat torus. We show their Hamiltonian structure and we then observe…

We consider the planar Taylor-Couette system for the steady motion of a viscous incompressible fluid in the region between two concentric disks, the inner one being at rest and the outer one rotating with constant angular speed. We study…

A global equilibrium state of a spin polarized fluid that undergoes constant acceleration along the stream lines is described as a solution of recently introduced perfect-fluid hydrodynamic equations with spin 1/2.

In this short paper we report on an inverse problem issued from a physical system, namely a fluid structure problem where the parameters are the rigidity constant, the solid-fluid density ratio and the fluid viscosity. We have chosen a…

We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…

This paper is concerned with steady vortex rings in an ideal fluid of uniform density, which are special global axi-symmetric solutions of the three-dimensional incompressible Euler equation. We systematically establish the existence,…

Using the Post-Minkowskian formalism and considering rotation as a perturbation, we compute an approximate interior solution for a stationary perfect fluid with constant density and axial symmetry. A suitable change of coordinates allows…

We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. We show that analytic mass functions describe a static regular centre in these coordinates. In this case, a central singularity can not be…

The necessary and sufficient conditions are obtained for a unit time-like vector field $u$ to be the unit velocity of a divergence-free perfect fluid energy tensor. This plainly kinematic description of a conservative perfect fluid requires…

We study adiabatic, radial perturbations of static, self-gravitating perfect fluids within the theory of general relativity employing a new perturbative formalism. We show that by considering a radially static observer, the description of…

We introduce two new static, spherically symmetric regular black hole solutions that can be obtained from non-linear electrodynamics models. For each solution, we investigate the dynamic stability with respect to arbitrary linear…

The problem of two stiff fluids (energy density = pressure) moving radially in spherical symmetry is treated. The metric ansatz is chosen spherically symmetric, conformally static with a multiplicative separation of variables. The first…

We discuss recent advances in the regularity problem of a variety of fluid equations and systems. The purpose is to illustrate the advantage of harmonic analysis techniques in obtaining sharper conditional regularity results when compared…

A global solution of the Einstein equations is given, consisting of a perfect fluid interior and a vacuum exterior. The rigidly rotating and incompressible perfect fluid is matched along the hypersurface of vanishing pressure with the…

We investigate the conformal geometry of spherically symmetric spacetimes in general without specifying the form of the matter distribution. The general conformal Killing symmetry is obtained subject to a number of integrability conditions.…