Related papers: Dynamical instability of minimal surfaces at flat …
Unstable minimal surfaces are the unstable stationary points of the Dirichlet-Integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used. The application of this…
We consider the Nernst-Planck-Stokes system on a bounded domain of $\mathbb{R}^d$, $d=2,3$ with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. It is well known that, in a wide range of cases, equilibrium…
We prove the Multiplicity One Conjecture for mean curvature flows of surfaces in $\mathbb{R}^3$. Specifically, we show that any blow-up limit of such mean curvature flows has multiplicity one. This has several applications. First, combining…
We describe the variation of the number $N(t)$ of spatial critical points of smooth curves (defined as a scalar distance $r$ from a fixed origin $O$) evolving under curvature-driven flows. In the latter, the speed $v$ in the direction of…
We construct examples of spherical space forms $(S^3/\Gamma,g)$ with positive scalar curvature and containing no stable embedded minimal surfaces, such that the following happens along the Ricci flow starting at $(S^3/\Gamma,g)$: a stable…
In their way to/from turbulence, plane wall-bounded flows display an interesting transitional regime where laminar and turbulent oblique bands alternate, the origin of which is still mysterious. In line with Barkley's recent work about the…
The set of volumes of stable surfaces does have accumulation points. In this paper, we study this phenomenon for surfaces with one cyclic quotient singularity, towards answering the question under which conditions we can still have…
Brakke flow is defined with a variational inequality, which means it may have discontinuous mass over time, i.e. have mass drop. It has long been conjectured that the Brakke flow associated to a nonfattening level set flow has no mass drop…
We study the evolution of local event-by-event deviations from smooth average fluid dynamic fields, as they can arise in heavy ion collisions from the propagation of fluctuating initial conditions. Local fluctuations around Bjorken flow are…
When turbulent flow is laden with negatively buoyant particles, their mean distribution over the direction of gravity can induce stable density gradients that penalize turbulent fluctuations. This effect is studied numerically for…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
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.…
The flow structures beneath waves have received significant attention from both theoretical and numerical perspectives. Most studies on this topic assume a flat bottom, leading to questions about the effects of variable bottom topography.…
We introduce a parabolic blow-up method to study the asymptotic behavior of an integral Brakke flow of planar networks (i.e. a 1-dimensional integral Brakke flow in a two dimensional region) weakly close in a space-time region to a static…
Hydrodynamic instability of a gravity-driven flow down an inclined plane is investigated in the presence of a floating elastic plate which rests on the top surface of the flow. Linear instability of the system with respect to infinitesimal…
Let $L_t$ be a zero Maslov, rational Lagrangian mean curvature flow in a compact Calabi-Yau surface, and suppose that at the first singular time a tangent flow is given by the static union of two transverse planes. We show that in this case…
The stability of a flow of an electrically conducting, incompressible fluid in a channel with an imposed uniform wall-normal magnetic field and electrically insulating walls is studied using linear stability analysis and direct numerical…
Upon decreasing the Reynolds number, plane Couette flow first forms alternately turbulent and laminar oblique bands out of featureless turbulence below some upper threshold R_t. These bands exist down to a global stability threshold R_g…
We study the stability of two-fluid flow through a plane channel at Reynolds numbers of a hundred to a thousand in the linear and nonlinear regimes. The two fluids have the same density but different viscosities. The fluids, when miscible,…
We show that the phase space of stratified turbulence mainly consists of two slow invariant manifolds with rich physics, embedded on a larger basin with fast evolution. A local invariant manifold in the vicinity of the fluid at equilibrium…