相关论文: Asymptotic behavior of regularized shock solutions…
The shock reflection problem is one of the most important problems in mathematical fluid dynamics, since this problem not only arises in many important physical situations but also is fundamental for the theory of multidimensional…
We show stability of spherical caps (SCs) lying on a flat surface, where the motion is governed by the volume-preserving Mean Curvature Flow (MCF). Moreover, we introduce a dynamic boundary condition that models a line tension effect on the…
A simplified, pseudoplastic rheology characterized by constant viscosity plateaus above and below a transition strain rate is applied to axisymmetric, gravitationally driven spreading of a thin fluid film with constant volume flux source in…
We consider arbitrary, possibly turbulent, Boussinesq flow which is smooth below a dissipative scale $l_d$. It is demonstrated that the stability of the flow with respect to growth of fluctuations with scale smaller than $l_d$ leads to a…
Since their development in 2001, regularised stokeslets have become a popular numerical tool for low-Reynolds number flows since the replacement of a point force by a smoothed blob overcomes many computational difficulties associated with…
We investigate the interaction of waves with surface flows by considering the full set of conserved quantities, subtle but important surface elevation changes induced by wave packets and by directly considering the necessary forces to…
The slip phenomena in thin polymer films confined by either flat or periodically corrugated surfaces are investigated by molecular dynamics and continuum simulations. For atomically flat surfaces and weak wall-fluid interactions, the shear…
We prove that the limit hypersurfaces of converging curvature flows are stable, if the initial velocity has a weak sign, and give a survey of the existence and regularity results.
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…
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…
Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of $N$ fluids with arbitrary viscosities, thicknesses, densities, and…
The dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime are examined. The challenging non-rectilinear mixed-boundary problem this poses is solved using a novel asymptotic approach and an asymptotic expansion…
We show that self-similar solutions for the mean curvature flow, surface diffusion and Willmore flow of entire graphs are stable upon perturbations of initial data with small Lipschitz norm. Roughly speaking, the perturbed solutions are…
We establish short-time existence of a smooth solution to the surface diffusion equation with an elastic term and without an additional curvature regularization in three space dimensions. We also prove the asymptotic stability of strictly…
By a combination of asymptotic ODE estimates and numerical Evans function calculations, we establish stability of viscous shock solutions of the isentropic compressible Navier--Stokes equations with $\gamma$-law pressure (i) in the limit as…
Recent experiments suggest that shear-enhanced growth of concentration fluctuations in polymer solutions is strongly influenced by solid boundaries. We analyze the dynamics of a model of a sheared polymer solution, accounting for the effect…
We investigate a steady flow of compressible fluid with inflow boundary condition on the density and slip boundary conditions on the velocity in a square domain in $\mathbf{R^2}$. We show existence of a strong solution $(v,\rho) \in…
Aims: Our aim is to investigate the resistive relaxation of a magnetic loop that contains braided magnetic flux but no net current or helicity. The loop is subject to line-tied boundary conditions. We investigate the dynamical processes…
We consider the anisotropic mean curvature flow of entire Lipschitz graphs. We prove existence and uniqueness of expanding self-similar solutions which are asymptotic to a prescribed cone, and we characterize the long time behavior of…