Related papers: On the Multi-Dimensional Divergence-Curl Problem a…
We consider conformal field theories with slightly broken higher spin symmetry in arbitrary spacetime dimensions. We analyze the crossing equation in the double light-cone limit and solve for the anomalous dimensions of higher spin currents…
We prove the existence of contact discontinuities for axisymmetric subsonic Euler flows with non-zero vorticity and non-zero angular momentum density in three-dimensional infinitely long cylinders. The problem is formulated as a two-phase…
In this paper we present a nonconforming finite element method for solving fourth order curl equations in three dimensions arising from magnetohydrodynamics models. We show that the method has an optimal error estimate for a model problem…
This paper is devoted to the problem of prescribing the scalar curvature under zero boundary conditions. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we…
We present a computational method to solve the magnetohydrodynamic equations in spherical geometry. The technique is fully nonlinear and wholly spectral, and uses an expansion basis that is adapted to the geometry: Chandrasekhar-Kendall…
We consider the nonlinear curl-curl problem $\nabla\times\nabla\times U + V(x) U=f(x,|U|^2)U$ in $\mathbb{R}^3$ related to the nonlinear Maxwell equations with Kerr-type nonlinear material laws. We prove the existence of a symmetric…
Local condition that imply the no-hair property of black holes are completed. The conditions take the form of constraints on the geometry of the 2-dimensional crossover surface of black hole horizon. They imply also the axial symmetry…
An algebraic background in order to study the integrability properties of pseudo-null curve motions in a $3$-dimensional Lorentzian space form is developed. As an application we delve into the relationship between the Burgers' equation and…
In this paper we show the non-uniqueness of mild solutions to the two-dimensional forced Navier-Stokes equations in the half space under the noslip boundary condition, following the program established by Albritton, Bru{\'e}, and Colombo in…
Cosmological dynamics of scalar field with a monomial potential $\phi^{n}$ with a general background equation of state is revisited. It is known that if $n$ is smaller than a critical value, the scalar field exhibits a coherent oscillation…
Pseudo-holomorphic curves on almost complex manifolds have been much more intensely studied than their "dual" objects, the plurisubharmonic functions. These functions are defined classically by requiring that the restriction to each…
We consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain $\Omega\subset\R^{n}$ whose boundary has an $(n-2)$-dimensional singularity. Assuming $1<p<\frac{n+2}{n-2}$, we prove that,…
The p-Laplace equation $$ \n \cdot (|\n u|^n \n u)=0 \whereA n>0, $$ in a bounded domain $\O \subset \re^2$, with inhomogeneous Dirichlet conditions on the smooth boundary $\p \O$ is considered. In addition, there is a finite collection of…
The deformation problem for pseudoholomorphic curves and related geometrical properties of the total moduli space of pseudoholomorphic curves are studied. A sufficient condition for the saddle point property of the total moduli space is…
We look for solutions $E:\Omega\to\mathbb{R}^3$ of the problem $$ \left\{ \begin{aligned} &\nabla\times(\nabla\times E) +\lambda E = |E|^{p-2}E &&\quad \text{in }\Omega &\nu\times E = 0 &&\quad \text{on }\partial\Omega \end{aligned} \right.…
Reformulating the incompressible Stokes equations with the velocity sought in H(curl) has recently emerged as a promising approach for the design of helicity-preserving schemes in magnetohydrodynamics and pressure-robust finite element…
We study general properties of the classical solutions in non-polynomial closed string field theory and their relationship with two dimensional conformal field theories. In particular we discuss how different conformal field theories which…
A generalized theory of two-dimensional isotropic turbulence is developed based on conformal symmetry. A number of minimal models of conformal turbulence are solved under an extended constraint including both the enstrophy cascade by…
This paper proposes direct and inverse results for the Dirichlet and Dirichlet to Neumann problems for complex curves with nodal type singularities. As an application, we give a method to reconstruct the conformal structure of a compact…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…