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In some problems of fluid mechanics, it is possible to be confronted with data that are not regular, that is why we are interested here in the search for the so-called very weak solutions for the stationary Stokes problem with Navier-type…
In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension - like, for example, the evolution of oil bubbles in water. Our main result is a weak-strong uniqueness principle…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, that its asymptotic behavior, when the distance between the two surfaces tends to…
We investigate the steady self-propelled motion of a rigid body immersed in a three-dimensional incompressible viscous fluid governed by the Navier-Stokes equations. The analysis is performed in a body-fixed reference frame, so that the…
We consider the two-dimensional Rayeigh-B\'enard convection problem between Navier-slip fixed-temperature boundary conditions and present a new upper bound for the Nusselt number. The result, based on a localization principle for the…
Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. We show how Prandtl's solution develops a…
We provide a rigorous derivation of the compressible Reynolds system as a singular limit of the compressible (barotropic) Navier-Stokes system on a thin domain. In particular, the existence of solutions to the Navier-Stokes system with…
An alternative form of the general solution of the linearized stationary Navier-Stokes equations for an incompressible fluid in spherical coordinates is obtained by the vector potential method. A previously published solution to this…
In this paper we are concerned with the steady Navier-Stokes and Stokes problems with mixed boundary conditions involving Tresca slip, leak condition, one-sided leak conditions, velocity, pressure, rotation, stress and normal derivative of…
We study a fluid-structure interaction problem describing movement of a rigid body inside a bounded domain filled by a viscous fluid. The fluid is modelled by the generalized incompressible Naiver-Stokes equations which include cases of…
We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…
In this paper, we investigate the instability of the trivial steady states to the incompressible viscous fluid with Navier-slip boundary conditions. For the linear instability, the existence of infinitely many normal mode solutions to the…
Recent experiments found that a hot solid sphere that is able to sustain a stable Leidenfrost vapour layer in a liquid exhibits significant drag reduction during free fall. The variation of the drag coefficient with Reynolds number shows…
Effective slip boundary conditions for flows over periodic micro-structured surfaces containing a secondary immiscible fluid are derived. The primary fluid is in the Cassie state, while the geometries of the micro-structures can be…
We study the high Reynolds number limit of a viscous fluid in the presence of a rough boundary. We consider the two-dimensional incompressible Navier-Stokes equations with Navier slip boundary condition, in a domain whose boundaries exhibit…
In Stokes flow, Purcell's scallop theorem forbids objects with time-reversible (reciprocal) swimming strokes from moving. In the presence of inertia, this restriction is eased and reciprocally deforming bodies can swim. A number of recent…
Hydrodynamic forces acting on a neutrally-buoyant spherical particle immersed in a wall-bounded axisymmetric stagnation point flow (Hiemenz-Homann flow) are predicted, based on a suitable form of the reciprocal theorem. An approximate…
We consider the flow of an { ideal} fluid in a 2D-bounded domain, admitting flows through the boundary of this domain. The flow is described by Euler equations with \textit{non-homogeneous } Navier slip boundary conditions. These conditions…
We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of…
The resolution of a very large class of linear and non-linear, stationary and evolutive partial differential problems in the half-space (or similar) under the slip boundary condition is reduced here to that of the corresponding results for…