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1.
In this paper we construct small-amplitude periodic capillary-gravity water waves with a piecewise constant vorticity distribution. They describe water waves traveling on superposed linearly sheared currents that have different vorticities. This is achieved by associating to the height function formulation of the water wave problem a diffraction problem where we impose suitable transmission conditions on each line where the vorticity function has a jump. The solutions of the diffraction problem, found by using local bifurcation theory, are the desired solutions of the hydrodynamical problem. 相似文献
2.
Joachim Escher Anca‐Voichita Matioc 《Mathematical Methods in the Applied Sciences》2013,36(11):1388-1398
In this paper, we consider a mathematical model describing the two‐phase interaction between water and mud in a water canal when the width of the canal is small compared with its depth. The mud is treated as a non‐Newtonian fluid, and the interface between the mud and fluid is allowed to move under the influence of gravity and surface tension. We reduce the mathematical formulation, for small boundary and initial data, to a fully nonlocal and nonlinear problem and prove its local well‐posedness by using abstract parabolic theory. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
3.
In this paper we consider the 2-dimensional flow of a Stokesian fluid in a Hele-Shaw cell. The motion of the flow is modelled
by a modified Darcy’s law. The existence of local solutions has been proved by the authors in a recent work, cf. [4]. The
purpose of this paper is to identify the steady states of this flow and to study their stability.
The equilibria will be identified as solutions of elliptic free boundary problems. It is shown that if the pressure on the
bottom is constant then the corresponding steady state is asymptotically stable.
相似文献
4.
Bogdan-Vasile Matioc 《Monatshefte für Mathematik》2014,174(3):459-475
We study periodic capillary and capillary-gravity waves traveling over a water layer of constant vorticity and finite depth. Inverting the curvature operator, we formulate the mathematical model as an operator equation for a compact perturbation of the identity. By means of global bifurcation theory, we then construct global continua consisting of solutions of the water wave problem which may feature stagnation points. A characterization of these continua is also included. 相似文献
5.
Bogdan-Vasile Matioc 《Archiv der Mathematik》2007,89(4):365-372
The motion of surfaces by their mean curvature has been studied by several authors from different points of view. K. A. Brake
studied this problem from the geometric measure theory point of view, the parametric problem was studied by G. Huisken [5].
Nonparametric mean curavture flow with boundary conditions was studied in [6] and [7]. Rotationally symmetric mean curvature
flows have been treated by G. Dziuk, B. Kawohl [3], but also by S. Altschuler, S. B. Angenent and Y. Giga [2].
In this paper we consider the case in which the initial surface has rotational symmetry and we shall generalize the results
in [3] in the sense that we shall give more general boundary conditions which enforce the formation of a singularity in finite
time. The proofs rely entirely on parabolic maximum principles.
Received: 6 September 2006 相似文献
6.
We use bifurcation theory to construct small periodic gravity stratified water waves with density which depends linearly upon the pseudostream function. As a special feature the density may also decrease with depth and the waves we obtain may posses two different critical layers with cat?s eye vortices. Within the vortex, the density of the fluid has an extremum at the stagnation point. 相似文献
7.
Joachim Escher Bogdan-Vasile Matioc 《NoDEA : Nonlinear Differential Equations and Applications》2013,20(3):539-555
In this paper we consider a strongly coupled fourth order parabolic system modelling the motion of two thin fluid layers in the presence of gravity and surface tension. In the non-degenerate case we prove existence and uniqueness of strong solutions and study the stability of the equilibria for various fluid–fluid configurations. 相似文献
8.
9.
Joachim Escher Anca-Voichita Matioc Bogdan-Vasile Matioc 《Journal of Mathematical Fluid Mechanics》2012,14(2):267-277
We consider the evolution of two thin fluid films in a porous medium. Starting from the classical equations modelling the Muskat problem we pass to the limit of small layer thickness and obtain a system of two coupled and degenerate parabolic equations for the films height. In the absence of surface tension forces we prove local well-posedness of the problem and show that the steady-states are exponentially stable. 相似文献
10.
We establish the existence of non-negative global weak solutions for a strongly coupled degenerated parabolic system which was obtained as an approximation of the two-phase Stokes problem driven solely by capillary forces. Moreover, the system under consideration may be viewed as a two-phase generalization of the classical Thin Film equation. 相似文献