相关论文: On 2D Euler Equations: Part II. Lax Pairs and Homo…
In the field of atomically thin 2D materials, oxides are relatively unexplored in spite of the large number of layered oxide structures amenable to exfoliation. There is an increasing interest in ultra-thin film oxide nanostructures from…
For a genuinely nonlinear $2\times 2$ hyperbolic system of conservation laws, assuming that the initial data have small ${\bf L}^\infty$ norm but possibly unbounded total variation, the existence of global solutions was proved in a…
Ordinary Differential Equations are derived for the adjoint Euler equations firstly using the method of characteristics in 2D. For this system of partial-differential equations, the characteristic curves appear to be the streamtraces and…
We study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has…
We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…
In this paper we prove that solutions of the 2D Euler equations in vorticity formulation obtained via vanishing viscosity approximation are renormalized.
\textit{Ab initio} calculations of electron-phonon interactions including the polar Fr\"ohlich coupling have advanced considerably in recent years. The Fr\"ohlich electron-phonon matrix element is by now well understood in the case of bulk…
The definition and properties of the Euler-Lagrange cohomology groups $H^{2k-1}$, $1 \leqslant k \leqslant n$, on a symplectic manifold $({\cal M}^{2n},\omega)$ are given and studied. For $k = 1$ and $k = n$, they are isomorphic to the…
Hodograph equations for the Euler equation in curved spaces with constant pressure are discussed. It is shown that the use of known results concerning geodesics and associated integrals allows to construct several types of hodograph…
Solutions $u(x)$ to the class of inhomogeneous nonlinear ordinary differential equations taking the form \[u'' + u^2 = \alpha f(x) \] for parameter $\alpha$ are studied. The problem is defined on the $x$ line with decay of both the solution…
Inspired by the numerical evidence of a potential 3D Euler singularity \cite{luo2014potentially,luo2013potentially-2}, we prove finite time blowup of the 2D Boussinesq and 3D axisymmetric Euler equations with smooth initial data of finite…
In this addendum note we fill in the gap left in \cite{ls} in the description of 2D homogeneous solutions to the stationary Euler system with the help of the results of \cite{sd}. This gives a complete classification of all solutions. The…
An example of a solution branch of the three dimensional Euler equation Cauchy problem is constructed which develops a singular velocity component and a singular vorticity component after finite time for some data which have Hoelder…
It is known that solutions to second order uniformly elliptic and parabolic equations, either in divergence or nondivergence (general) form, are H\"{o}lder continuous and satisfy the interior Harnack inequality. We show that even in the…
In this paper, we study the logarithmically regularized $2$D Euler system \eqref{e1}, which is derived by regularizing the Euler equation for the vorticity. We establish local well-posedness of the logarithmically regularized $2$D Euler…
In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are perturbations of annular equilibria, in contrast to the laminar…
In n-dimensional Euclidean space E^n, harmonic curvatures of a non-degenerate curve defined by \"Ozdamar and Hacisaliho\u{g}lu [4]. In this paper, We define a new type of curves called LC helix when the angle between tangent of this curve…
Common two-dimensional (2D) materials have a layered 3D structure with covalently bonded, atomically thin layers held together by weak van der Waals forces. However, in a recent transmission electron microscopy experiment, atomically thin…
We present a general method to obtain the stable lasing solutions for the steady-state ab-initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2d). We find that under most regimes (with one…
We study numerically the time evolution of two-dimensional (2D) domain patterns in proper tetragonal-orthorhombic (T-O) ferroelastics. Our results, found by solving equations of motion derived from classical elasticity theory, disagree with…