Related papers: Shock interaction in sphere symmetry
This paper deals with the spherically symmetric flow of compressible viscous and polytropic ideal fluid in unbounded domain exterior to a ball in $\mathbb{R}^n$ with $n\ge2$. We show that the global solutions are convergent as time goes to…
We present a new method for studying equilibrium properties of interacting fluids in an arbitrary external field. The fluid is composed of monodisperse spherical particles with hard-core repulsion and additional interactions of arbitrary…
We perform direct numerical simulations of shock-wave/boundary-layer interactions (SBLI) at Mach number M = 1.7 to investigate the influence of the state of the incoming boundary layer on the interaction properties. We reproduce and extend…
We provide exact solutions of the Stokes equations for a squirming sphere close to a no-slip surface, both planar and spherical, and for the interactions between two squirmers, in three dimensions. These allow the hydrodynamic interactions…
This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation…
A spherically symmetric charged ideal fluid solution of Einstein field equation is given in the presence of the cosmological constant and two well known example of this type of solution is presented. If the matter is confined in a region,…
The problem of hydrogen neutrals interacting with the heliospheric bow shock region has received considerable attention recently, motivated primarily by the hope that the Voyager spacecraft may soon encounter the first of the heliospheric…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…
Spiral waves are investigated in oscillatory media exhibiting period-doubling bifurcations. In the period-doubled and chaotic regimes, the rotational symmetry of the spiral wave is broken. The loss of symmetry takes the form of…
We prove that spacetime is locally inertial at points of shock wave collision in General Relativity. The result applies for collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes.…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
Arrangement of interacting particles on a sphere is historically a well known problem, however, ordering of particles with anisotropic interaction, such as the dipole-dipole interaction, has remained unexplored. We solve the orientational…
In this paper we consider the direct scattering problem of obliquely incident time-harmonic electromagnetic plane waves by an infinitely long dielectric cylinder. We assume that the cylinder and the outer medium are homogeneous and…
The problem of a cold gas flowing past a stationary object is considered. It is shown that at large distances from the obstacle the shock front forms a parabolic solid of revolution. The interior of the shock front is obtained by solution…
We consider the problem of a rotating charged spherical shell of radius a carrying an axially symmetric distribution of charge. We give the interior and exterior solutions to this problem for arbitrary zonal dependence of the surface charge…
In this work we developed a new problem solution methodology of contact interaction of acoustic medium with resilient finite bodies of cylindrical form, based on application of boundary integral equations method in conjunction with series…
This work is concerned with the finiteness problem for static, spherically symmetric perfect fluids in both Newtonian Gravity and General Relativity. We derive criteria on the barotropic equation of state guaranteeing that the corresponding…
We analyze the interpretation of the spherically symmetric perfect fluid solutions that admit a flat synchronization orthogonal to the fluid flow as a thermodynamic perfect fluid in local thermal equilibrium. The ideal gas sonic condition…
An impulsively starting motion of two cylindrical bodies floating on a free liquid surface is considered. The shape of the cross-section of each body and the distance between them is arbitrary. The integral hodograph method is advanced to…
We consider the two-dimensional capillary-gravity water waves problem where the free surface $\Gamma_t$ intersects the bottom $\Gamma_b$ at two contact points. In our previous works \cite{MW2, MW3}, the local well-posedness for this problem…