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This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider orbital motion in transverse plane for a single…
We investigate Kato's method for parabolic equations with a quadratic non-linearity in an abstract form. We extract several properties known from linear systems theory which turn out to be the essential ingredients for the method. We give…
Note that some classic fluid dynamical systems such as the Navier-Stokes equations, Magnetohydrodynamics (MHD), Boussinesq equations, and etc are observably different from each other but obey some energy inequalities of the similar type. In…
The present paper reviews recent advances in the theory of nonlinear driven magnetohydrodynamic (MHD) waves in slow and Alfven resonant layers. Simple estimations show that in the vicinity of resonant positions the amplitude of variables…
I summarize our recent work towards finding and utilizing analytic solutions of relativistic hydrodynamic. In the first part I discuss various exact solutions of the second-order conformal hydrodynamics. In the second part I compute flow…
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…
This paper establishes a regularity theory for the magnetohydrodynamics (MHD) equations with external forces through scaling analysis. Inspired by the existing methodology, we utilize linearized approximations and the monotonicity property…
In the present paper we focus on building simple nonperturbative analytical relativistic models of magnetars. With this purpose in mind we first develop a method for generating exact interior solutions to the static and axisymmetric…
Through a discussion of some typical unsteady hydrodynamic flows, we argue that the time averaged hydrodynamic functions at each point give a rather sparse filling of the local jet space. This situation then suggests a set of time dependent…
We obtain an exact solution of the self-consistent relativistic magnetohydrodynamic equations for an anisotropic magnetoactive plasma in the background of a plane gravitational wave metric (PGW) with an arbitrary polarization. It is shown…
We have derived the full set of MHD equations for incompressible shear flow of a magnetized fluid and considered their solution in the wave-vector space. The linearized equations give the famous amplification of slow magnetosonic waves and…
This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
Introduction: the Navier-Stokes equations are essential in fluid dynamics, describing the motion of fluids like liquids and gases. Solving these equations, especially in complex flows and high-Reynolds-number regimes, is a significant…
We present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary…
This paper provides primarily an analytical ad hoc -solution for 3-dimensional, incompressible Navier-Stokes equations with a suitable external force field. The solution turns out to be smooth and integrable on the whole space. There is…
We present in this note the existence and uniqueness results for the Stokes and Navier-Stokes equations which model the laminar flow of an incompressible fluid inside a two-dimensional channel of periodic sections. The data of the pressure…
In many astrophysical plasmas, the Coulomb collision is insufficient to maintain an isotropic temperature, and the system is driven to the anisotropic regime. In this case, magnetohydrodynamic (MHD) models with anisotropic pressure are…
We establish the existence and uniqueness of solutions to an abstract nonlinear equation driven by a multiplicative noise of L\'evy type, which covers many hydrodynamical models including 2D Navier-Stokes equations, 2D MHD equations, the 2D…