相关论文: Shallow water equations on a fast rotating surface
In this paper, we study the stationary magnetohydrodynamics system in $\mathbb{R}^2\times\mathbb{T}$. We prove trivialness of D-solutions (the velocity field $u$ and the magnetic field $h$) when they are swirl-free. Meanwhile, this…
We introduce a technique to solve numerically the relativistic Euler's equations in scenarios with spherical symmetry using the standard Smoothed Particles Hydrodynamics method in cartesian coordinates. This implementation allow us to…
In this paper, we prove the existence and uniqueness of the solutions for the 2D viscous shallow water equations with low regularity assumptions on the initial data as well as the initial height bounded away from zero.
We derive and analyze well-posed, energy- and entropy-stable boundary conditions (BCs) for the two-dimensional linear and nonlinear rotating shallow water equations (RSWE) in vector invariant form. The focus of the study is on subcritical…
We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…
We consider the linearized 2D inviscid shallow water equations in a rectangle. A set of boundary conditions is proposed which make these equations well-posed. Several different cases occur depending on the relative values of the reference…
Shallow flows are governed by the Navier-Stokes equations. They are commonly modelled using the shallow water equations, a great simplification of the Navier-Stokes equations, which often yields inaccurate results. For that reason, a model…
The paper deals with the large time asymptotic of the fundamental solution for a time fractional evolution equation for a convolution type operator. In this equation we use a Caputo time derivative of order $\alpha$ with $\alpha\in(0,1)$,…
We study continuous dependence of solutions to quasilinear evolution equations of parabolic-type in the framework of maximal $L^p$-regularity. For equations of the form \[ \frac{d\phi}{dt} + A(t,\phi)\phi = f(t,\phi), \] we establish…
The majority of coastal flows are characterized by turbulence, rendering the application of shallow water equations an inadequate approach for their accurate description. This paper presents a theory for characterizing accelerated coastal…
We consider the motion of ideal incompressible fluid with free surface. We analyzed the exact fluid dynamics though the time-dependent conformal mapping $z=x+iy=z(w,t)$ of the lower complex half plane of the conformal variable $w$ into the…
The problem of two stiff fluids (energy density = pressure) moving radially in spherical symmetry is treated. The metric ansatz is chosen spherically symmetric, conformally static with a multiplicative separation of variables. The first…
Using the generalised set of fluid equations that include the `Coriolis force' along with the centrifugal and pressure gradient forces, we have reanalysed the class of self similar solutions, with the pseudo-Newtonian potential. We find…
In this paper we address the return to equilibrium problem for an axisymmetric floating structure in shallow water. First we show that the equation for the solid motion can be reduced to a delay differential equation involving an…
We study the generalized point-vortex problem and the Gross-Pitaevskii equation on surfaces of revolution. We find rotating periodic solutions to the generalized point-vortex problem, which have two two rings of $n$ equally spaced vortices…
We consider the evolution of hypersurfaces on the unit sphere $\mathbb{S}^{n+1}$ by smooth functions of the Weingarten map. We introduce the notion of `quasi-ancient' solutions for flows that do not admit non-trivial, convex, ancient…
We develop, via Arnold's geometric framework, a mechanism for constructing explicit, smooth, global-in-time, and typically non-stationary solutions of the incompressible Euler equations. The approach introduces a notion of generalized…
We prove that if a solution of the discrete time-dependent Schr\"odinger equation with bounded real potential decays fast at two distinct times then the solution is trivial. For the free Shr\"odinger operator and for operators with…
In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form \begin{equation*} \partial_t u + \partial_x(\Lambda^s u + u\Lambda^r u^2) = 0, \end{equation*} where…
In this paper we construct periodic capillarity-gravity water waves with an arbitrary bounded vorticity distribution. This is achieved by reexpressing, in the height function formulation of the water wave problem, the boundary condition…