相关论文: Active vector models generalizing 3D Euler and ele…

The quasi-geostrophic two-layer (QS2L) system models the dynamic evolution of two interconnected potential vorticities, each is governed by an active scalar equation. These vorticities are linked through a distinctive combination of their…

Magnetohydrodynamics (MHD) describes the interaction between electrically conducting fluids and electromagnetic fields. We propose and analyze a symplectic, second-order algorithm for the evolutionary MHD system in Els\"asser variables. We…

The Voigt regularization is a technique used to model turbulent flows, offering advantages such as sharing steady states with the Navier-Stokes equations and requiring no modification of boundary conditions; however, the parabolic…

Given a weight two modular form f with associated p-adic Galois representation V_f, for certain quadratic imaginary fields K one can construct canonical classes in the Galois cohomology of V_f by taking the Kummer images of Heegner points…

Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…

In this paper we study the global regularity of the following 2D (two-dimensional) generalized magnetohydrodynamic equations \begin{eqnarray*} \left\{\begin{array}{llll} u_t + u \cdot \nabla u & = & - \nabla p + b \cdot \nabla b - \nu…

We show that weak solutions to the 3D quasi-geostrophic system in the class $C^\zeta_{t,x}$ for $\zeta<\frac{1}{5}$ are not unique and may achieve any smooth, non-negative energy profile. Our proof follows a convex integration scheme which…

The development of smooth particle magnetohydrodynamic (SPMHD) has significantly improved the simulation of complex astrophysical processes. However, the preservation the solenoidality of the magnetic field is still a severe problem for the…

A certain generalisation of the hierarchy of mKdV equations (modified KdV), which forms an integrable system, is studied here. This generalisation is based on a Lax operator associated to the equations, with principal components of degrees…

We establish the well/ill-posedness theories for the inviscid $\alpha$-surface quasi-geostrophic ($\alpha$-SQG) equations in H\"older spaces, where $\alpha = 0$ and $\alpha = 1$ correspond to the two-dimensional Euler equation in the…

We show that the following three systems related to various hydrodynamical approximations: the Korteweg--de Vries equation, the Camassa--Holm equation, and the Hunter--Saxton equation, have the same symmetry group and similar bihamiltonian…

We study regularity properties of the data-to-solution maps of the family of generalized surface quasi-geostrophic equations which includes both the 2D incompressible Euler and the standard surface quasi-geostrophic equations. We prove that…

The Euler-Koszul complex is the fundamental tool in the homological study of A-hypergeometric differential systems and functions. We compare Euler-Koszul homology with D-module direct images from the torus to the base space through orbits…

New generalized equations of motion for the Weber-Clebsch potentials that describe both the Navier-Stokes and MHD dynamics are derived. These depend on a new parameter, which has dimensions of time for Navier-Stokes and inverse velocity for…

We investigate the nonlocal version of the Abels-Garcke-Gr\"{u}n (AGG) system, which describes the motion of a mixture of two viscous incompressible fluids. This consists of the incompressible Navier-Stokes-Cahn-Hilliard system…

This paper deals with the global well-posedness of the 3D axisymmetric Euler equations for initial data lying in some critical Besov spaces

We investigate the well-posedness of $\alpha$-SQG equations in the half-plane, where $\alpha=0$ and $\alpha=1$ correspond to the 2D Euler and SQG equations respectively. For $0<\alpha \le 1/2$, we prove local well-posedness in certain…

We present a dynamical spectral model for Large Eddy Simulation of the incompressible magnetohydrodynamic (MHD) equations based on the Eddy Damped Quasi Normal Markovian approximation. This model extends classical spectral Large Eddy…

Let $U$ be a connected open subset of $\mathbb{R}^n$, and let $X=(X_1,X_{2},\ldots,X_m)$ be a system of H\"{o}rmander vector fields defined on $U$. This paper addresses sharp embedding results and geometric inequalities in the generalized…

In this paper, we investigate a class of inviscid generalized surface quasi-geostrophic (SQG) equations on the half-plane with a rigid boundary. Compared to the Biot-Savart law in the vorticity form of the 2D Euler equation, the velocity…