相关论文: Beltrami fields with a nonconstant proportionality…
A measurable function $\mu$ on the unit disk $\mathbb{D}$ of the complex plane with $\|\mu\|_\infty<1$ is sometimes called a Beltrami coefficient. We say that $\mu$ is trivial if it is the complex dilatation $f_{\bar z}/f_z$ of a…
It is shown that the universal steady Euler flow field, independent of boundary shape or symmetry, in a toroidal domain with fixed boundary obeys a nonlinear Beltrami equation, with the nonlinearity arising from a Boltzmann-like,…
We prove that the correspondence between Reeb and Beltrami vector fields can be made equivariant whenever additional symmetries of the underlying geometric structures are considered. As a corollary of this correspondence, we show that…
We consider ($-\alpha$)-homogeneous solutions to the stationary incompressible Euler equations in $\mathbb{R}^{3}\backslash\{0\}$ for $\alpha\geq 0$ and in $\mathbb{R}^{3}$ for $\alpha<0$. Shvydkoy (2018) demonstrated the nonexistence of…
Consider the nonlinear scalar field equation \begin{equation} \label{a1} -\Delta{u}= f(u)\quad\text{in}~\mathbb{R}^N,\qquad u\in H^1(\mathbb{R}^N), \end{equation} where $N\geq3$ and $f$ satisfies the general Berestycki-Lions conditions. We…
We investigate the existence, uniqueness, and $L^1$-contractivity of weak solutions to a porous medium equation with fractional diffusion on an evolving hypersurface. To settle the existence, we reformulate the equation as a local problem…
The solutions of traditional fractional differential equations neither satisfy group property nor generate dynamical systems, so the study on hyperbolicity is in blank. Relying on the new proposed conformable fractional derivative, we…
In this paper, Beltrami vector fields in several orthogonal coordinate systems are obtained analytically and numerically. Specifically, axisymmetric incompressible inviscid steady state Beltrami (Trkalian) fluid flows are obtained with the…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
We study the specification property for partially hyperbolic dynamical systems. In particular, we show that if a partially hyperbolic diffeomorphism has two saddles with different indices, and stable manifold of one of them coincides with…
The freedom in choosing finite renormalizations in quantum field theories (QFT) is characterized by a set of parameters $\{c_i \}, i = 1 ..., n >...$, which specify the renormalization prescriptions used for the calculation of physical…
Object of the present paper is the local theory of solution for steady ideal Euler flows and ideal MHD equilibria. The present analysis relies on the Lie-Darboux theorem of differential geometry and the local theory of representation and…
We consider foliations of compact complex manifolds by analytic curves. We suppose that the line bundle tangent to the foliation is negative. We show that in a generic case there exists a finitely smooth homeomophism, holomorphic on the…
Understanding complexity in fluid mechanics is a major problem that has attracted the attention of physicists and mathematicians during the last decades. Using the concept of renormalization in dynamics, we show the existence of a locally…
In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a…
For a generic value of the central charge, we prove the holomorphic factorization of partition functions for free superconformal fields which are defined on a compact Riemann surface without boundary. The partition functions are viewed as…
We show that every homeomorphic $W^{1,1}_{\rm loc}$ solution $f$ to a Beltrami equation $\bar{\partial}f=\mu \partial f$ in a domain $D\subset\Bbb C$ is the so--called lower $Q-$homeomorphism with $Q(z)=K^T_{\mu}(z, z_0)$ where…
The Hodge equations for 1-forms are studied on Beltrami's projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for…
There are many topological faces of the superfluid phases of $^3$He. These superfluids contain various topological defects and textures. The momentum space topology of these superfluids is also nontrivial, as well as the topology in the…
In this paper we show that the homeomorphic solutions to each nonlinear Beltrami equation $\partial_{\bar{z}} f = \mathcal{H}(z, \partial_{z} f)$ generate a two-dimensional manifold of quasiconformal mappings $\mathcal{F}_{\mathcal{H}}…