Related papers: Singularities in axisymmetric free boundaries for …

We consider singular solutions to quasilinear elliptic equations under zero Dirichlet boundary condition. Under suitable assumptions on the nonlinearity we deduce symmetry and monotonicity properties of positive solutions via an improved…

In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem), for which the smoothness of the interface breaks down…

In this paper we study isentropic flow in a curved pipe. We focus on the consequences of the geometry of the pipe on the dynamics of the flow. More precisely, we present the solution of the general Cauchy problem for isentropic fluid flow…

For the water waves equations, the existence of splat singularities has been shown in [3], i.e., the interface self-intersects along an arc in finite time. The aim of this paper is to show the absence of splat singularities for the…

We develop a model of an electrorheological fluid such that the fluid is considered as an anisotropic one with the viscosity depending on the second invariant of the rate of strain tensor, on the module of the vector of electric field…

In this paper, we consider the wave equation on an n-dimensional simplex with Dirichlet boundary conditions. Our main result is an asymptotic observability identity from any one face of the simplex. The novel aspects of the result are that…

We show that the water waves system is locally wellposed in weighted Sobolev spaces which allow for interfaces with corners. No symmetry assumptions are required. These singular points are not rigid: if the initial interface exhibits a…

The problem of determining equilibrium configurations of the free surface of a conducting liquid is considered with allowance for a finite interelectrode distance. The analogy is established between this electrostatic problem and that of…

We examine static perfect fluid spheres in the presence of a cosmological constant. New exact matter solutions are discussed which require the Nariai metric in the vacuum region. We generalize the Einstein static universe such that neither…

This study explores singularity-free solutions to the static, spherical symmetric Einstein equations with the standard Schwarzschild solution as a boundary condition. Imposing the absence of curvature singularities and requiring…

We study a 2D potential flow of an ideal fluid with a free surface with decaying conditions at infinity. By using the conformal variables approach, we study a particular solution of Euler equations having a pair of square-root branch points…

We study the motion of charged liquid drop in three dimensions where the equations of motions are given by the Euler equations with free boundary with an electric field. This is a well-known problem in physics going back to the famous work…

For ideal fluid flow with zero surface tension and gravity, it remains unknown whether local singularities on the free surface can develop in well-posed initial value problems with smooth initial data. This is so despite great advances over…

Both k-essence and the pressureless perfect fluid develop caustic singularities at finite time. We further explore the connection between the two and show that they belong to the same class of models, which admits the caustic free…

We show that there exist asymptotically flat almost-smooth initial data for Einstein-perfect fluid's equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and…

In the study of low-speed or low-Froude flows of a potential gravity-driven fluid past a wave-generating object, the traditional asymptotic expansion in powers of the Froude number predicts a waveless free-surface at every order. This is…

In this paper, a system of one-dimensional gas dynamics equations is considered. This system is a particular case of Jacobi type systems and has a natural representation in terms of 2-forms on 0-jet space. We use this observation to find a…

Two collective properties distinguishing the thin liquid water vapour interface from the bulk liquid are the anisotropy of the pressure tensor giving rise to surface tension and the orientational alignment of the molecules leading to a…

We consider the Gross-Pitaevskii equation describing a dipolar Bose-Einstein condensate without external confinement. We first consider the unstable regime, where the nonlocal nonlinearity is neither positive nor radially symmetric and…

It is well-known that the unit cotangent bundle of any Riemannian manifold has a canonical contact structure. A surface in a Riemannian 3-manifold is called a (wave) front if it is the projection of a Legendrian immersion into the unit…