Related papers: Vanishing viscosity limit for concentrated vortex …
We study the time evolution of an incompressible fluid with axisymmetry without swirl when the vorticity is sharply concentrated. In particular, we consider $N$ disjoint vortex rings of size $\varepsilon$ and intensity of the order of…
We study the time evolution of an incompressible fluid with axial symmetry without swirl, assuming initial data such that the initial vorticity is very concentrated inside $N$ small disjoint rings of thickness $\varepsilon$ and vorticity…
We study the time evolution of an incompressible fluid with axial symmetry without swirl when the vorticity is sharply concentrated on $N$ annuli of radii $\approx$ $r_0$ and thickness $\epsilon$. We prove that when $r_0= |\log…
We study the time evolution of an incompressible fluid with axial symmetry without swirl when the vorticity is sharply concentrated on $N$ annuli of radii of the order of $r_0$ and thickness $\varepsilon$. We prove that when $r_0= |\log…
We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [LMN], on the vanishing viscosity limit of circularly symmetric viscous flow in a disk with rotating boundary, shown there to converge to the inviscid limit in $L^2$-norm…
We consider an incompressible fluid with axial symmetry without swirl, assuming initial data such that the initial vorticity is very concentrated inside $N$ small disjoint rings of thickness $\varepsilon$, each one of vorticity mass and…
The incompressible Navier-Stokes equations in R^3 are shown to admit a unique axisymmetric solution without swirl if the initial vorticity is a circular vortex filament with arbitrarily large circulation Reynolds number. The emphasis is on…
We study the vanishing viscosity limit for the three-dimensional incompressible Navier-Stokes equations in terms of the relative vorticity in the setting of axisymmetric velocity fields without swirl. We show that the weak convergence of…
In the present paper we study the fast rotation limit for viscous incompressible fluids with variable density, whose motion is influenced by the Coriolis force. We restrict our analysis to two dimensional flows. In the case when the initial…
The paper is concerned with the vanishing viscosity limit of the two-dimensional degenerate viscous lake equations when the Navier slip conditions are prescribed on the impermeable boundary of a simply connected bounded regular domain. When…
For the incompressible Navier-Stokes equations in $R^3$ with low viscosity $\nu>0$, we consider the Cauchy problem with initial vorticity $\omega_0$ that represents an infinitely thin vortex filament of arbitrary given strength $\Gamma$…
In this paper we study the evolution of a small rigid body in a viscous incompressible fluid, in particular we show that a small particle is not accelerated by the fluid in the limit when its size converges to zero under a lower bound on…
In this paper, we investigate the uniform regularity and vanishing limit for the incompressible nematic liquid crystal flows in three dimensional bounded domain. It is shown that there exists a unique strong solution for the incompressible…
We consider the evolutionary MHD systems, and study the the regularity and vanishing viscosity limit of the 3-D viscous system in a class of bounded domains with a slip boundary condition. We derive the convergence is in H^{2k+1}, for k>0,…
We consider axisymmetric incompressible inviscid flows without swirl in $\mathbb{R}^3$, under the assumption that the axial vorticity is non-positive in the upper half space and odd in the last coordinate, which corresponds to the flow…
In this paper, we are concerned with nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler fluids. We focus on the case when the vorticity function has a simple discontinuity, which corresponding to a…
Theoretical results on water waves almost always start by assuming irrotationality of the flow in order to simplify the formulation. In this work, we investigate the well-foundedness of this hypothesis via numerical simulations of the…
We show strong convergence of the vorticities in the vanishing viscosity limit for the incompressible Navier-Stokes equations on the two-dimensional torus, assuming only that the initial vorticity of the limiting Euler equations is in $L^p$…
In this paper, we consider the small viscosity limit problem for the isentropic compressible Navier-Stokes equations in a 2D exterior domain with impermeable boundary conditions , and the corresponding Euler equations have vortex sheet…
In this paper we study concentrated solutions of the three-dimensional Euler equations in helical symmetry without swirl. We prove that any helical vorticity solution initially concentrated around helices of pairwise distinct radii remains…