JMP: Fluids

The Biot-Savart operator and electrodynamics on subdomains of the three-sphere

Jason Parsley
We study steady-state magnetic fields in the geometric setting of positive curvature on subdomains of the three-dimensional sphere. By generalizing the Biot-Savart law to an integral operator BS acting on all vector fields, we show that electrodynamics in such a setting behaves rather similarly to E ... [J. Math. Phys. 53, 013102 (2012)] published Fri Jan 13, 2012.

Vortex dynamics in [openface R]

Banavara N. Shashikanth
The vortex dynamics of Euler's equations for a constant density fluid flow in [openface R] is studied. Most of the paper focuses on singular Dirac delta distributions of the vorticity two-form omega in [openface R]. These distributions are supported on two-dimensional surfaces termed membranes and a ... [J. Math. Phys. 53, 013103 (2012)] published Fri Jan 13, 2012.

Non-uniform dependence for a modified Camassa-Holm system

Guangying Lv and Mingxin Wang
This paper is concerned with the non-uniform dependence on initial data for a modified Camassa-Holm system. We prove that the solution map of the Cauchy problem of the Camassa-Holm system is not uniformly continuous in H([openface R]), s > 1. Moreover, we obtain the similar result for the initial bo ... [J. Math. Phys. 53, 013101 (2012)] published Thu Jan 5, 2012.

On polygonal relative equilibria in the N-vortex problem

M. Celli, E. A. Lacomba, and E. Perez-Chavela
Helmholtz's equations provide the motion of a system of N vortices which describes a planar incompressible fluid with zero viscosity. A relative equilibrium is a particular solution of these equations for which the distances between the vortices are invariant during the motion. In this article, we f ... [J. Math. Phys. 52, 103101 (2011)] published Fri Oct 7, 2011.

Global strong solution for a three-dimensional viscous liquid-gas two-phase flow model with vacuum

Zhenhua Guo, Jing Yang, and Lei Yao
This paper is concerned with the Cauchy problem of the 3D viscous liquid-gas two-phase flow model, where the initial vacuum is allowed. The existence of the global strong solution is proved when the energy of the initial data is small enough. ... [J. Math. Phys. 52, 093102 (2011)] published Fri Sep 16, 2011.

Internal heating driven convection at infinite Prandtl number

Jared P. Whitehead and Charles R. Doering
We derive an improved rigorous lower bound on the space and time averaged temperature of an infinite Prandtl number Boussinesq fluid contained between isothermal no-slip boundaries driven by uniform internal heating. A singular stable stratification is introduced as a perturbation to a non-singular ... [J. Math. Phys. 52, 093101 (2011)] published Fri Sep 16, 2011.

L-bounds for quasi-geostrophic equations via functional analysis

Rafael de la Llave and Enrico Valdinoci
We give a proof of L-bounds for the quasi-geostrophic equation and other non-local equations. The proof uses mainly tools from functional analysis, notably the product formulas (also known as operator splitting methods) and the Bochner-Pollard subordination identities, hence it could be applicable t ... [J. Math. Phys. 52, 083101 (2011)] published Thu Aug 11, 2011.

Some Serrin-type regularity criteria for weak solutions to the Navier-Stokes equations

Zujin Zhang, Zheng-an Yao, Ming Lu, and Lidiao Ni
We consider the regularity criteria for a weak solution u=(u,u,u) to the Navier-Stokes equations in [openface R]. Denoting by omega=(omega,omega,omega)=curl u the vorticity, we then prove that u is smooth, provided u, omega; or [partial-derivative]u, omega are in some Serrin-type integrability clas ... [J. Math. Phys. 52, 053103 (2011)] published Tue May 24, 2011.

Model for laminar and turbulent flows of viscous and nonlinear viscous non-Newtonian fluids

W. G. Litvinov
We develop a model that describes laminar and turbulent flows of viscous and nonlinear viscous fluids. A basis for the model is a characteristic, which we call a local Reynolds number, and which is calculated at each point of the domain of flow. In the subdomain wherein the local Reynolds number doe ... [J. Math. Phys. 52, 053102 (2011)] published Fri May 13, 2011.

Length-scale estimates for the 3D simplified Bardina magnetohydrodynamic model

Davide Catania
We consider the MHD-alpha model known as double viscous simplified Bardina MHD (SBMHD) on a 3D periodic box (MHD stands for magnetohydrodynamic). This system is a large eddy simulation model useful to approximate the turbulent behavior of an incompressible homogeneous magnetofluid because of the act ... [J. Math. Phys. 52, 053101 (2011)] published Thu May 12, 2011.

Lie symmetry analysis and exact solutions of the quasigeostrophic two-layer problem

Alexander Bihlo and Roman O. Popovych
The quasigeostrophic two-layer model is of superior interest in dynamic meteorology since it is one of the easiest ways to study baroclinic processes in geophysical fluid dynamics. The complete set of point symmetries of the two-layer equations is determined. An optimal set of one- and two-dimension ... [J. Math. Phys. 52, 033103 (2011)] published Tue Mar 29, 2011.

A regularity criterion for the three-dimensional nematic liquid crystal flow in terms of one directional derivative of the velocity

Qiao Liu, Jihong Zhao, and Shangbin Cui
In this paper we provide a sufficient condition for regularity of solutions to the 3D nematic liquid crystal flow in the entire space in terms of one directional derivative of the velocity field. More precisely, we prove that if [partial-derivative]u belongs to L(0,T;L([openface R])) with (3/(alpha) ... [J. Math. Phys. 52, 033102 (2011)] published Thu Mar 17, 2011.

Nonuniform dependence for the Cauchy problem of the general b-equation

Yan Li
This paper is concerned with the nonuniform dependence on initial data for the general b-equation. We prove that the solution map of the Cauchy problem of the b-equation is not uniformly continuous in H([openface R]), s > 3/2. ... [J. Math. Phys. 52, 033101 (2011)] published Fri Mar 11, 2011.

The model with many moments for relativistic electron beams: A simplified solution

Maria Cristina Carrisi and Sebastiano Pennisi
In the 1980s, Amendt and Weitzner proposed an interesting model capable to describe relativistic electron beams. It concerned 14 independent variables and the closure was obtained by using the entropy and the Einstein relativity principles. As we know from literature, an extension to many moments al ... [J. Math. Phys. 52, 023103 (2011)] published Fri Feb 25, 2011.

Global smooth solutions for 1D thermally radiative magnetohydrodynamics

Yuming Qin and Guili Hu
This paper is concerned with the global existence of smooth solutions to equations describing one-dimensional motion of a self-gravitating, radiative of magnetohydrodynamics gas. We have proved that for any arbitrary large smooth initial data, the problem under consideration admits a unique globally ... [J. Math. Phys. 52, 023102 (2011)] published Thu Feb 24, 2011.

Well-posedness for the viscous rotating shallow water equations with friction terms

Chengchun Hao
We consider the Cauchy problem for viscous rotating shallow water equations with friction terms. The global existence of the solution in some hybrid spaces is shown for the initial data close to a constant equilibrium state away from the vacuum. ... [J. Math. Phys. 52, 023101 (2011)] published Thu Feb 17, 2011.

Homogenization of the linearized ionic transport equations in rigid periodic porous media

Gregoire Allaire, Andro Mikelic, and Andrey Piatnitski
In this paper we undertake the rigorous homogenization of a system of partial differential equations describing the transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid porous medium. The motion is governed by a small static electric field and a small hydrodynamic for ... [J. Math. Phys. 51, 123103 (2010)] published Thu Dec 30, 2010.

Exact solution to the general Riemann problem in nonuniform and nonstationary media: A simplified analysis of a shock wave accelerated at a constant rate

Koichi Mori
Exact solutions to special cases of the general Riemann problem, in which two nonuniform and nonstationary flows are initially separated by a discontinuity at the origin, are proposed. By describing the evolution of flows using a family of the group-invariant solutions derived by Ovsiannikov [Dokl. ... [J. Math. Phys. 51, 123102 (2010)] published Wed Dec 29, 2010.

Blow-up solutions of the general b-equation

Guangying Lv and Mingxin Wang
In this short paper, we consider the b-equation. A new precise blow-up scenario is described and some new results are obtained for the blow-up phenomena. ... [J. Math. Phys. 51, 123101 (2010)] published Thu Dec 23, 2010.

Green tensors for DebyeBucheBrinkman equations generalized for axisymmetric medium

Bogdan Cichocki and Maria L. Ekiel-Jezewska
A fluid flow through a nonisotropic porous medium with an axial symmetry is considered. The Green tensors for the corresponding nonisotropic DebyeBucheBrinkman equations are calculated in terms of single integrals. Short-distance and far-field limiting behavior is discussed. The exact solution for t ... [J. Math. Phys. 51, 103101 (2010)] published Tue Oct 26, 2010.

On the existence of vortexlike solutions in the auroral F-region

A. M. Hamza
In this paper we construct a set of nonlinear coupled partial differential equations governing the evolution of plasma fluctuations as they occur in the ionospheric auroral F region. The nonlinear system of equations is shown to support a set of stationary vortexlike solutions. It is also shown that ... [J. Math. Phys. 51, 093102 (2010)] published Wed Sep 22, 2010.