Related papers: On 3-D vortex patches in bounded domains
In the paper we study the 2D div-curl problem in the exterior domain which models the flow with given vorticity, divergency, boundary condition at infinity, and Dirichlet condition on the solid surface. We will find the relations on…
Mathematical model of the turbulent flux in the three-layer boundary system is presented. Turbulence is described as a presence of the nonzero vorticity. Generalized advection-diffusion-reaction equation is derived for arbitrary number…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in $\R^3$ with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the…
We consider the motion of several solids in a bounded cavity filled with a perfect incompressible fluid, in two dimensions. The solids move according to Newton's law, under the influence of the fluid's pressure, and the fluid dynamics is…
An effort has been made to solve the Cauchy problem of the Navier-Stokes equations in the whole space by two methods. It is proved that the sum of the three vorticity components is a time-invariant in fluid motion. It has been proved that,…
We consider $L^2$ minimizing geodesics along the group of volume preserving maps $SDiff(D)$ of a given 3-dimensional domain $D$. The corresponding curves describe the motion of an ideal incompressible fluid inside $D$ and are (formally)…
We consider the smooth, compactly supported solutions of the steady 3D Euler equations of incompressible fluids constructed by Gavrilov in 2019, and we study the corresponding fluid particle dynamics. This is an ode analysis, which…
A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time…
We study an evolution problem in the space of continuous loops in three-dimensional Euclidean space modelled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local solution starting…
Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements.…
We construct a family of rotating vortex patches with fixed angular velocity for the two-dimensional Euler equations in a disk. As the vorticity strength goes to infinity, the limit of these rotating vortex patches is a rotating point…
In this article, we study Lions' density patch problem in two space dimensions at critical regularity. We prove global existence, uniqueness, and stability for a fluid occupying a bounded Lipschitz region surrounded by vacuum and evolving…
In this paper we study a coupled system modeling the movement of a deformable solid immersed in a fluid. For the solid we consider a given deformation that has to obey several physical constraints. The motion of the fluid is modeled by the…
A fluid flow in a multiply connected domain generated by an arbitrary number of point vortices is considered. A stream function for this flow is constructed as a limit of a certain functional sequence using the method of images. The…
In this paper, we prove nonlinear stability of planar vortex patches concentrated near an isolated minimum point of the Robin function in a general bounded domain. These vortex patches are stationary solutions of the two-dimensinal…
We develop a neutral vortex fluid theory on closed surfaces with zero genus. The theory describes collective dynamics of many well-separated quantum vortices in a superfluid confined on a closed surface. Comparing to the case on a plane,…
The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…
In order to describe behavior of various liquid-like materials at high pressures, incompressible fluid models with pressure dependent viscosity seem to be a suitable choice. In the context of implicit constitutive relations involving the…
The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation.…
We analyze the steady motion of a viscous incompressible fluid in a three-dimensional channel containing an obstacle through the Navier-Stokes equations with mixed boundary conditions: the inflow is given by a fairly general datum and the…