相关论文: Can We Remove Secular Terms for Analytical Solutio…
A new class of analytical 2-D solutions of the full set of the steady magnetohydrodynamic (MHD) equations, describing an axisymmetric helicoidal magnetized outflow originating from a rotating central object, is presented. The solutions are…
We consider the Boussinesq equation on the line for a broad class of Schwartz initial data for which (i) no solitons are present, (ii) the spectral functions have generic behavior near $\pm 1$, and (iii) the solution exists globally. In a…
We study the three-dimensional, incompressible, non-hydrostatic Boussinesq fluid equations, which are applicable to the dynamics of the oceans and atmosphere. These equations describe the interplay between velocity and buoyancy in a…
Homotopy perturbation method is used for solving the multi-point boundary value problems. The approximate solution is found in the form of a rapidly convergent series. Several numerical examples have been considered to illustrate the…
We investigate a hydrodynamic equation system which - with some approximation - is capable to describe the tsunami propagation in the open ocean with the time-dependent self-similar Ansatz. We found analytic solutions how the wave height…
A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…
We study the excitation and damping of tides in close binary systems, accounting for the leading order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct effects: three-mode nonlinear interactions…
This paper presents a combined field and boundary integral equation method for solving the time-dependent scattering problem of a thermoelastic body immersed in a compressible, inviscid and homogeneous fluid. The approach here is a…
This article concludes the study of (2+1)-dimensional nonlinear wave equations that can be derived in a model of an ideal fluid with irrotational motion. In the considered case of identical scaling of the $x,y$ variables, obtaining a…
We address the linear-mode analysis performed near an equilibrium configuration in the fluid rest frame with a dynamical magnetic field perturbed on a constant configuration. We develop a simple and general algorithm for an analytic…
A generalized equation is constructed for a class of classical oscillators with strong anharmonicity which are not exactly solvable. Aboodh transform based homotopy perturbation method (ATHPM) is applied to get the approximate analytical…
We consider an isotropic compressible non-dissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid as well as the free…
We obtained steady solutions to the two-dimensional Boussinesq approximation equations without mean temperature gradient. This system is referred to as free convection in this paper. Under an external flow described by the stream function…
In this paper, we study the Cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms. As is pointed out by [8], in this combination, the frictional damping term is dominant for the viscoelastic one for the…
In this paper we argue that differential rotation can possibly sustain hydrodynamic turbulence in the absence of magnetic field. We explain why the non-linearities of the hydrodynamic equations (i.e. turbulent diffusion) should not be…
Nonlinear effects are crucial in order to compute the cosmological matter power spectrum to the accuracy required by future generation surveys. Here, a new approach is presented, in which the power spectrum, the bispectrum and higher order…
We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation…
We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…
A new numerical method is developed to approximate the solution of Laplace's equation in the exterior of the sphere with a strongly nonlinear boundary value of oblique type. A functional analysis attempt to solve this type of boundary…
We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted…