Related papers: On well-posedness, stability, and bifurcation for …
Advection-dominated accretion flows (ADAFs) are known to be convectively unstable for low values of the viscosity parameter alpha. Two-dimensional axisymmetric hydrodynamic simulations of such flows reveal a radial density profile which is…
We analyze the stability of a cylindrical Couette flow under the imposition of a weak axial flow in case of a very short cylinder with a narrow annulus gap. We consider an incompressible viscous fluid which is contained in the narrow gap…
In this paper we investigate the flow of surfaces by a class of symmetric functions of the principal curvatures with a mixed volume constraint. We consider compact surfaces without boundary that can be written as a graph over a sphere. The…
A problem in nonlinear water-wave propagation on the surface of an inviscid, stationary fluid is presented. The primary surface wave, suitably initiated at some radius, is taken to be a slowly evolving nonlinear cylindrical wave (governed…
We study constant mean curvature Lorentzian hypersurfaces of $\mathbb{R}^{1,d+1}$ from the point of view of its Cauchy problem. We completely classify the spherically symmetric solutions, which include among them a manifold isometric to the…
We study the rescaled mean curvature flow (MCF) of hypersurfaces that are global graphs over a fixed cylinder of arbitrary dimensions. We construct an explicit stable manifold for the rescaled MCF of finite codimensions in a suitable…
With few exceptions, known explicit solutions of the curve shortening flow (CSE) of a plane curve, can be constructed by classical Lie point symmetry reductions or by functional separation of variables. One of the functionally separated…
We present analytic solutions for steady flow of the Johnson-Segalman (JS) model with a diffusion term in various geometries and under controlled strain rate conditions, using matched asymptotic expansions. The diffusion term represents a…
Stable diffusion, a generative model used in text-to-image synthesis, frequently encounters resolution-induced composition problems when generating images of varying sizes. This issue primarily stems from the model being trained on pairs of…
We consider viscous steady streaming induced by oscillatory flow past a cylinder between two plates, where the cylinder's axis is normal to the plates. While this phenomenon was first studied in the 1930s, it has received renewed interest…
We present the results of numerical integrations yielding the structure of and meridional flow in axisymmetric thin viscous accretion disk models. The solutions are obtained by simplifying and approximating first the equations, using…
We show the existence of a smooth solution for the flow deformed by the square root of the scalar curvature multiplied by a positive anisotropic factor $\psi$ given a strictly convex initial hypersurface in Euclidean space suitably pinched.…
We investigate the motion of a family of closed curves evolving according to the geometric evolution law on a given two dimensional manifold which is embedded or immersed in the three-dimensional Euclidean space. We derive a system of…
We investigate the flat flow solution for the surface diffusion equation via the discrete minimizing movements scheme proposed by Cahn and Taylor. We prove that in dimension three the scheme converges to the unique smooth solution of the…
A model for axisymmetric magnetized accretion flow is proposed. The dominant mechanism of energy dissipation is assumed to be the magnetic diffusivity due to turbulence in the accretion flow. In analogy to the advection-dominated accretion…
This paper concerns the structural stability of smooth cylindrically symmetric supersonic Euler-Poisson flows in nozzles. Both three-dimensional and axisymmetric perturbations are considered. On one hand, we establish the existence and…
Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions.…
Flow and Diffusion Distributed Structures (FDS) are stationary spatially periodic patterns that can be observed in reaction-diffusion-advection systems. These structures arise when the flow rate exceeds a certain bifurcation point provided…
In this article we consider the inviscid two-dimensional shallow water equations in a rectangle. The flow occurs near a stationary solution in the so called supercritical regime and we establish short term existence of smooth solutions for…
We analyze both numerically and experimentally the stability of the steady jetting tip streaming produced by focusing a liquid stream with another liquid current when they coflow through the orifice of an axisymmetric nozzle. We calculate…