Related papers: A calculus for flows in periodic domains
In this paper, we propose a method of fundamental solutions for the problem of two-dimensional potential flow in a doubly-periodic domain. The solution involves a doubly-periodic function, to which it is difficult to give an approximation…
In this paper, we propose a method of fundamental solutions for the problems of two-dimensional potential flow past a doubly-periodic array of obstacles. The solutions of these problems involve doubly-periodic functions, and it is difficult…
This paper is devoted to describe the finite-dimensionality of a two-dimensional micropolar fluid flow with periodic boundary conditions. We define the notions of determining modes and nodes and estimate the number of them, we also estimate…
Coupled triple well (phi6) one-dimensional potentials occur in both condensed matter physics and field theory. Here we provide a set of exact periodic solutions in terms of elliptic functions (domain wall arrays) and obtain single domain…
The method of reduction of a Fredholm integral equation to the linear system is generalized to construction of a complex potential --- an analytic function in an infinite multiply connected domain with a simple pole at infinity which maps…
Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so…
Coupled asymmetric double well ($a\phi^2-b\phi^3+c\phi^4$) one-dimensional potentials arise in the context of first order phase transitions both in condensed matter physics and field theory. Here we provide an exhaustive set of exact…
Recent experiments on mucociliary clearance, an important defense against airborne pathogens, have raised questions about the topology of two-dimensional (2D) flows. We introduce a framework for studying ensembles of 2D time-invariant flow…
Consider a free boundary problem of compressible-incompressible two-phase flows with surface tension and phase transition in bounded domains $\Omega_{t +}, \Omega_{t -} \subset \mathbb{R}^N$, $N \ge 2$, where the domains are separated by a…
We study a 2D potential flow of an ideal fluid with a free surface with decaying conditions at infinity. By using the conformal variables approach, we study a particular solution of Euler equations having a pair of square-root branch points…
Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…
We consider an elliptic pseudo differential equation in a multi-dimensional cone and starting wave factorization concept we add some boundary conditions. For the simplest cases explicit formulas for solution are given like layer potentials…
We consider the 1-harmonic flow of maps from a bounded domain into a submanifold of a Euclidean space, i.e. the gradient flow of the total variation functional restricted to maps taking values in the manifold. We restrict ourselves to…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
In this paper, we establish some local and global solutions for the two phase incompressible inhomogeneous flows with moving interfaces in $L_p-L_q$ maximal regularity class. Compared with previous results obtained by V.A.Solonnikov and by…
A fluid flow in a multiply connected domain generated by an arbitrary number of point vortices is considered. A stream function for this flow is constructed as a limit of a certain functional sequence using the method of images. The…
In this paper we consider the incompressible 2D Euler equation in an annular domain with non-penetration boundary condition. In this setting, we prove the existence of a family of non-trivially smooth time-periodic solutions at an…
In this study we revisit the problem of computing steady Navier-Stokes flows in two-dimensional unbounded domains. Precise quantitative characterization of such flows in the high-Reynolds number limit remains an open problem of theoretical…
We consider the two-phase flow model with slip boundary condition in a 3D exterior domains whose boundary is smooth. We establish the global existence of classical solutions of this system provided that the initial energy is suitably small.…
We present a set of effective outflow/open boundary conditions and an associated algorithm for simulating the dynamics of multiphase flows consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids in domains involving outflows or…