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The Cauchy problem for the two dimensional Euler–Poisson system

Dong Li, Yifei Wu (2014)

Journal of the European Mathematical Society

The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo [7] first constructed a global smooth irrotational solution by using the dispersive Klein-Gordon effect. It has been conjectured that same results should hold in the two-dimensional case. In our recent work [13], we proved the existence of a family of smooth solutions by constructing the wave operators for the 2D system....

The Cauchy problem for viscous shallow water equations.

Weike Wang, Chao-Jiang Xu (2005)

Revista Matemática Iberoamericana

In this paper we study the Cauchy problem for viscous shallow water equations. We work in the Sobolev spaces of index s > 2 to obtain local solutions for any initial data, and global solutions for small initial data.

The dispersion of gas exhalations and the problem of distribution of new sources on a dry hilly surface

Dien Hien Tran (1986)

Aplikace matematiky

The process of gas exhalations in the lower layer of the atmosphere and the problem of distribution of new sources of exhalations in a hilly terrain are studied. Among other, the following assumptions are introduced: (1) the terrain is a hilly one, (2) the exhalations enter a chemical reaction with the atmosphere, (3) the process is stationary, (4) the vector of wind velocity satisfies the continuity equation. The mathematical formulation of the problem then is a mixed boundary value problem for...

The dock problem revisited.

Chakrabarti, A., Mandal, B.N., Gayen, Rupanwita (2005)

International Journal of Mathematics and Mathematical Sciences

The effect of a magnetic field on the onset of Bénard convection in variable viscosity couple-stress fluids using classical Lorenz model

Venkatesh Ramachandramurthy, Nagasundar Kavitha, Agrahara Sanjeevmurthy Aruna (2022)

Applications of Mathematics

The Rayleigh-Bénard convection for a couple-stress fluid with a thermorheological effect in the presence of an applied magnetic field is studied using both linear and non-linear stability analysis. This problem discusses the three important mechanisms that control the onset of convection; namely, suspended particles, an applied magnetic field, and variable viscosity. It is found that the thermorheological parameter, the couple-stress parameter, and the Chandrasekhar number influence the onset of...

The Effect of Crystal-Melt Surface Energy on the Stability of Ultra-Thin Melt Films

M. Beerman, L. N. Brush (2008)

Mathematical Modelling of Natural Phenomena

The stability and evolution of very thin, single component, metallic-melt films is studied by analysis of coupled strongly nonlinear equations for gas-melt (GM) and crystal-melt (CM) interfaces, derived using the lubrication approximation. The crystal-melt interface is deformable by freezing and melting, and there is a thermal gradient applied across the film. Linear analysis reveals that there is a maximum applied far-field temperature in the gas, beyond which there is no film instability. Instabilities...

The effective boundary conditions for vector fields on domains with rough boundaries: Applications to fluid mechanics

Eduard Feireisl, Šárka Matušů-Nečasová (2011)

Applications of Mathematics

The Navier-Stokes system is studied on a family of domains with rough boundaries formed by oscillating riblets. Assuming the complete slip boundary conditions we identify the limit system, in particular, we show that the limit velocity field satisfies boundary conditions of a mixed type depending on the characteristic direction of the riblets.

Currently displaying 21 – 40 of 209