Related papers: Boundary regularity of rotating vortex patches

Using group theory arguments and numerical simulations, we demonstrate the possibility of changing the vorticity or topological charge of an individual vortex by means of the action of a system possessing a discrete rotational symmetry of…

In the present contribution, we first prove the existence of $\mathbf{m}$-fold simply-connected V-states close to the unit disc for Euler-$\alpha$ equations. These solutions are implicitly obtained as bifurcation curves from the circular…

We consider a class of one-dimensional quantum spin systems on the finite lattice $\Lambda\subset\mathbb{Z}$, related to the XXZ spin chain in its Ising phase. It includes in particular the so-called droplet Hamiltonian. The entanglement…

We consider a diffuse interface approximation for the lipid phases of rotationally symmetric two-phase bilayer membranes and rigorously derive its $\Gamma$-limit. In particular, we prove that limit vesicles are $C^1$ across interfaces,…

We prove that in finite time a trajectory of a Lipschitz vector field in $\hbox{\bbbb R}^{\hbox{\tmm n}}$ can not have infinite rotation around a given point. This result extends to the mutual rotation of two trajectories of a field in…

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 $\Gamma$…

Using pseudoholomorphic curves techniques from symplectic geometry, Barney Bramham proved recently that every smooth irrational pseudo-rotation of the unit disk is the limit, for the $C^0$ topology, of a sequence of smooth periodic…

Regularity and singularity of the solutions according to the shape of domains is a challenging research theme in the Boltzmann theory (\cite{Kim11,GKTT1}). In this paper, we prove an H\"older regularity in $C^{0,\frac{1}{2}-}_{x,v}$ for the…

We establish optimal $C^s$ boundary regularity for the most general class of (linear and translation invariant) nonlocal elliptic operator of order $2s$. Namely, we consider L\'evy operators that are symmetric and its Fourier symbol…

We study the process of vortex nucleation in rotating two-dimensional BEC confined in a harmonic trap. We show that, within the Gross-Pitaevskii theory with the boundary condition of vanishing of the order parameter at infinity, topological…

This work is the sequel of a previous investigation of stationary and cylindrically symmetric vortex configurations for simple models representing an incompressible non-relativistic superconductor in a rigidly rotating background. In the…

We prove sharp boundary H{\"o}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini}}$-property. This result is new even for the fractional…

We study a class of two-phase inhomogeneous free boundary problems governed by elliptic equations in divergence form. In particular we prove that Lipschitz or flat free boundaries are $C^{1,\gamma}$. Our results apply to the classical…

We prove that the boundary of a (not necessarily connected) bounded smooth set with constant nonlocal mean curvature is a sphere. More generally, and in contrast with what happens in the classical case, we show that the Lipschitz constant…

In this paper, we prove the existence of relative equilibria with holes for quasi-geostrophic shallow-water equations. More precisely, using bifurcation techniques, we establish for any m large enough the existence of two branches of m-fold…

The geometric properties of domains are well-known to be crucial factors influencing the regularity of Boltzmann boundary problems. In the presence of non-convex physical boundaries, highly singular behaviors are investigated including the…

We consider a bounded Lipschitz domain $\Omega\subseteq\mathbb{R}^3$ with sufficiently smooth boundary and prove piecewise Sobolev regularity of vector fields that have piecewise regular curl and divergence, but may be discontinuous across…

Let $\mathcal{B}$ be a compact convex planar domain with smooth boundary of finite type and $\mathcal{B}_\theta$ its rotation by an angle $\theta$. We prove that for almost every $\theta\in[0, 2\pi]$ the remainder…

In this paper, we study the boundary regularity for viscosity solutions of parabolic $p$-Laplace type equations. In particular, we obtain the boundary pointwise $C^{1,\alpha}$ regularity and global $C^{1,\alpha}$ regularity.

We observe the transient formation of a ringed pattern state during spin-up of an evaporating fluid on a time scale of order a few Ekman spin-up times. The ringed state is probed using infrared thermometry and particle image velocimetry and…