Related papers: Steady vortex patches near a nontrivial irrotation…
This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a rigid plane and with an upper boundary given by a free surface. The fluid is subject to a constant external force with a horizontal component, which…
We consider inviscid flow with isentropic coefficient greater than one. For flow along smooth infinite protruding corners we attempt to impose a nonzero limit for velocity at infinity at the upstream wall. We prove that the problem does not…
We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…
We study the behaviour of heavy inertial particles in the flow field of two like-signed vortices. In a frame co-rotating with the two vortices, we find that stable fixed points exist for these heavy inertial particles; these stable…
This paper addresses the problem of axisymetric rotating flows bounded by a fixed horizontal plate and subject to a permanent, uniform, vertical magnetic field (the so-called B\"odewadt-Hartmann problem). The aim is to find out which one of…
We give an overview on the solution of the stationary Navier-Stokes equations for non newtonian incompressible fluids established by G. Dias and M.M. Santos (Steady flow for shear thickening fluids with arbitrary fluxes, J. Differential…
The inviscid multi-layer quasi-geostrophic equations are considered over an arbitrary bounded domain. The no-flux but non-homogeneous boundary conditions are imposed to accommodate the free fluctuations of the top and layer interfaces.…
In this paper we construct small amplitude periodic internal waves traveling at the boundary region between two rotational and homogeneous fluids with different densities. Within a period, the waves we obtain have the property that the…
In a system of point vortices, there exist regions of stability around each vortex, even if the system is chaotic. These regions are usually called stability islands and they have a morphology that is hard to characterise. We study and…
In this paper, we analyze the behavior of a family of solutions of a nonlinear elliptic equation with nonlinear boundary conditions, when the boundary of the domain presents a highly oscillatory behavior which is uniformly Lipschitz and…
In this paper, the steady creeping flow equations of a second grade fluid in cartesian coordinates are considered; the equations involve a small parameter related to the dimensionless non--Newtonian coefficient. According to a recently…
Based on the solution of Atanasiu et al. (2004), a theoretical model for axisymmetric vortex flows is derived in the present study by solving the vorticity transport equation for an inviscid, incompressible fluid in cylindrical coordinates.…
We provide high-order approximations to periodic travelling wave profiles and to the velocity field and the pressure beneath the waves, in flows with constant vorticity over a flat bed.
We study the stationary nonhomogeneous Navier--Stokes problem in a two dimensional symmetric domain with a semi-infinite outlet (for instance, either parabo-\\loidal or channel-like). Under the symmetry assumptions on the domain, boundary…
Using complementary numerical approaches at high resolution, we study the late-time behaviour of an inviscid, incompressible two-dimensional flow on the surface of a sphere. Starting from a random initial vorticity field comprised of a…
We consider the superfluid phase of a specific renormalizable relativistic quantum field theory. We prove that, within the regime of validity of perturbation theory and of the superfluid effective theory, there are consistent and regular…
The purpose of this work is to discuss the well-posedness theory of singular vortex patches. Our main results are of two types: well-posedness and ill-posedness. On the well-posedness side, we show that globally $m-$fold symmetric vortex…
In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an…
Significant advancements have emerged in the theory of asymptotic stability of shear flows in stably stratified fluids. In this comprehensive review, we spotlight these recent developments, with particular emphasis on novel approaches that…
In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…