Related papers: Notes on Symmetry in Convective Flows
The aim of this work is to study the Navier-Stokes-Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated non-linear initial-and boundary-value problem, we prove the…
We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…
In this talk we show a stiff fluid solution of the Einstein equations for a cylindrically symmetric spacetime. The main features of this metric are that it is non-separable in comoving coordinates for the congruence of the worldlineS of the…
Symmetry-breaking bifurcations, where a flow state with a certain symmetry undergoes a transition to state with a different symmetry, are ubiquitous in fluid mechanics. Much can be understood about the nature of these transitions from…
In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are perturbations of annular equilibria, in contrast to the laminar…
We consider the Euler equations governing relativistic compressible fluids evolving in the Minkowski spacetime with several spatial variables. We propose a new symmetrization which makes sense for solutions containing vacuum states and, for…
The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid…
A cantilever beam under axial flow, confined or not, is known to develop self-sustained oscillations at sufficiently large flow velocities. In recent decades, the analysis of this archetypal system has been mostly pursued under linearized…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
Instabilities driven by strong gradients appear in a wide variety of physical systems, including plasmas, neutral fluids, and self-gravitating systems. This work develops an analytic formulation to describe the transport structure and…
In this paper, we present an analytical study, in the one space dimensional case, of the fluid dynamics system proposed in [4] to model the formation of biofilms. After showing the hyperbolicity of the system, we show that, in a open…
This work is devoted to the study of a class of linear time-inhomogeneous evolution equations in a scale of Banach spaces. Existence, uniquenss and stability for classical solutions is provided. We study also the associated dual Cauchy…
We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…
We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…
When subcritical shear flows transition to turbulence, laminar and turbulent flow often coexists in space, giving rise to turbulent-laminar patterns. Most prominent are regular stripe patterns with large-scale periodicity and oblique…
Steady flows of an incompressible homogeneous chemically reacting fluid are described by a coupled system, consisting of the generalized Navier--Stokes equations and convection - diffusion equation with diffusivity dependent on the…
The classical Benjamin and Lighthill conjecture about steady water waves states that the non-dimensional flow force constant of a solution is bounded by the corresponding constants of the supercritical and subcritical uniform streams…
The so-called 'direct' approach to separation of variables in linear PDEs is applied to the hydrodynamic stability problem. Calculations are made for the complete linear stability equations in cylindrical coordinates. Several classes of the…
We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform…
We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find pinching conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions…