相关论文: On an Elliptic Free Boundary Problem and Subsonic …

We propose a method of construction of exact solutions of free boundary problems corresponding to Hele-Shaw flows in presence of an external field. Such a field may arise, in particular, due to electrokinetic phenomena. Both a general…

In this paper, we prove the existence and uniqueness of subsonic solutions to the steady Euler flows past a smooth, axisymmetric obstacle. Specifically, for a broad class of prescribed positive axial velocities in the upstream, the subsonic…

We derive an effective boundary condition for granular flow taking into account the effect of the heterogeneity of the force network on sliding friction dynamics. This yields an intermediate boundary condition which lies in the limit…

We investigate the formation of acoustic horizons for an inviscid fluid moving in a pipe in the case of stationary and axi-symmetric flow. We show that, differently from what is generally believed, the acoustic horizon forms in…

Supersonic jet noise reduction is important for high speed military aircraft. Lower acoustic levels would reduce structural fatigue leading to longer lifetime of the jet aircraft. It is not solely structural aspects which are of importance,…

We consider a rigid body freely moving in a compressible inviscid fluid within a bounded domain $\Omega\subset\mathbb{R}^3$. The fluid is thereby governed by the non necessarily isentropic compressible Euler equations, while the rigid body…

In this paper, we study the global existence of steady subsonic Euler flows through infinitely long nozzles which are periodic in $x_1$ direction with the period $L$. It is shown that when the variation of Bernoulli function at some given…

We consider a Boussinesq system describing one-dimensional internal waves which develop at the boundary between two immiscible fluids, and we restrict to its traveling waves. The method which yields explicitly all the elliptic or degenerate…

The influence of the bending rigidity of a flexible heaving wing on its propulsive performance in a two-dimensional imposed parallel flow is investigated in the inviscid limit. Potential flow theory is used to describe the flow over the…

A free boundary problem for the dynamics of a glasslike binary fluid naturally leads to a singular perturbation problem for a strongly degenerate parabolic partial differential equation in 1D. We present a conjecture for an asymptotic…

Direct numerical simulations of free round jets at a Reynolds number ($Re_{D}$) of $5000$, based on jet diameter ($D$) and jet-exit bulk velocity ($U_{e}$), are performed to study jet turbulence characteristics at supercritical pressures.…

We determine the asymptotic spreading speed of an invasive species, which invades the territory of a native competitor, governed by a diffusive competition model with a free boundary in a spherically symmetric setting. This free boundary…

We study an initial-boundary-value problem for time-dependent flows of heat-conducting viscous incompressible fluids in a system of three-dimensional pipes on a time interval $(0,T)$. Here we are motivated by the bounded domain approach…

We study the free boundary Euler equations in two spatial dimensions. We prove that if the boundary is sufficiently regular, then solutions of the free boundary fluid motion converge to solutions of the Euler equations in a fixed domain…

Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, resulting flows in an unbounded two-dimensional incompressible…

We consider the free boundary incompressible porous media equation which describes the dynamics of a density transported by a Darcy flow in the field of gravity, with a free boundary between the fluid region and the dry region above it. For…

Free surface, axially symmetric shallow flow is analysed in both the centrifugal and centripetal directions. Referring to the inviscid steady flow over a flat plate characterised by a unique value of specific energy, the analytical sub- and…

We analyze the tunneling of vortex states from elliptically shaped traps. Using the hydrodynamic representation of the Gross-Pitaevskii (Nonlinear Schr\"odinger) equation, we derive analytically and demonstrate numerically a novel type of…

We derive a set of equations in conformal variables that describe a potential flow of an ideal inviscid fluid with free surface in a bounded domain. This formulation is free of numerical instabilities present in the equations for the…

In this paper, we are concerned with the structural stability of some steady subsonic solutions for Euler-Poisson system. A steady subsonic solution with subsonic background charge is proven to be structurally stable with respect to small…