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In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in [50] is a…
A deep understanding of the physical interactions between nanoparticles and target cell membranes is important in designing efficient nanocarrier systems for drug delivery applications. Here, we present a theoretical framework to describe…
The detailed mathematical study of the recent paper by Sajjadi, Hunt and Drullion (2014) is pre- sented. The mathematical developement considered by them, for unsteady growing monochro- matic waves is also extended to Stokes waves. The…
There has been significant recent interest in the study of water waves coupled with non-zero vorticity. We derive analytical approximations for the exponentially-small free-surface waves generated in two-dimensions by one or several…
We report on progress on the free surface flow in the presence of submerged oscillating line sources (2D) or point sources (3D) when a simple shear flow is present varying linearly with depth. Such sources are in routine use as Green…
We examine the exponentially improved asymptotic expansion of the Lerch zeta function $L(\lambda,a,s)=\sum_{n=1}^\infty \exp (2\pi ni\lambda)/(n+a)^s$ for large complex values of $a$, with $\lambda$ and $s$ regarded as parameters. It is…
In this paper we study non stationary viscous incompressible fluid flows with nonlinear boundary slip conditions given by a subdifferential property of friction type. More precisely we assume that the tangential velocity vanishes as long as…
Analytical expressions for the velocity field and the effective slip length of pressure-driven Stokes flow through slippery pipes and annuli with rotationally symmetrical longitudinal slits are derived. Specifically, the developed models…
In this paper, we consider a stationary, constant viscosity, incompressible Stokes flow with singular forces along one or several interfaces. Assuming only the jumps of the pressure are present along the interface, we develop a new…
The Reynolds equation from lubrication theory and the Stokes equations for zero Reynolds number flows are distinct models for an incompressible fluid with negligible inertia. Here we investigate the sensitivity of the Reynolds equation to…
In this thesis we consider the free surface flow due to a submerged source in a channel of finite depth. This problem has been considered previously in the literature, with some disagreement about whether or not a train of waves exist on…
A method is proposed to estimate the velocity field of an unsteady flow using a limited number of flow measurements. The method is based on a non-linear low-dimensional model of the flow and on expanding the velocity field in terms of…
Stokes wave is a finite amplitude periodic gravity wave propagating with constant velocity in inviscid fluid. Complex analytical structure of Stokes wave is analyzed using a conformal mapping of a free fluid surface of Stokes wave into the…
We revisit and present new linear spaces of explicit solutions to incompressible Euler and Navier-Stokes equations on $\mathbb{R}^n$, as well as the rotating Boussinesq equations on $\mathbb{R}^3$. We cast these solutions are superpositions…
We consider the quasistationary Stokes flow that describes the motion of a two-dimensional fluid body under the influence of surface tension effects in an unbounded, infinite-bottom geometry. We reformulate the problem as a fully nonlinear…
This paper presents an efficient coupling of the 3D Stokes flow interacting with an effective perforated periodic heterogeneous anisotropic 2D plate. The effective model was obtained by the asymptotic analysis in earlier works and here an…
We study the two-phase Stokes flow driven by surface tension with two fluids of equal viscosity, separated by an asymptotically flat interface with graph geometry. The flow is assumed to be two-dimensional with the fluids filling the entire…
In the paper we study the impact of the boundary vorticity distribution on the dynamics of enstrophy for flows around streamlined body. A new energy identity is derived in the article, which includes the boundary values of the vortex…
In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior…
Complex analytical structure of Stokes wave for two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth is analyzed. Stokes wave is the fully nonlinear periodic gravity wave propagating with the…