相关论文: Optimal Prandtl expansion around concave boundary …

Building on work of Barker, Humpherys, Lafitte, Rudd, and Zumbrun in the shock wave case, we study stability of compressive, or "shock-like", boundary layers of the isentropic compressible Navier-Stokes equations with gamma-law pressure by…

We consider graphical solutions to mean curvature flow and obtain a stability result for homothetically expanding solutions coming out of cones of positive mean curvature: If another solution is initially close to the cone at infinity, then…

We consider the flow of an upper convected Maxwell fluid in the limit of high Weissenberg and Reynolds number. In this limit, the no-slip condition cannot be imposed on the solutions. We derive equations for the resulting boundary layer and…

We establish the well-posedness of the MHD boundary layer system in Gevrey function space without any structural assumption. Compared to the classical Prandtl equation, the loss of tangential derivative comes from both the velocity and…

Dependence of boundary layer thickness on layer height in laminar and transient regimes is studied for convection from localised heat source with an open surface. The measurements of Nusselt number and characteristic frequency of thermal…

We survey some aspects of stability conditions both in general and on the derived category of coherent sheaves on a surface, with applications to the birational geometry of certain holomorphic symplectic varieties.

We consider the mean curvature flow of compact convex surfaces in Euclidean $3$-space with free boundary lying on an arbitrary convex barrier surface with bounded geometry. When the initial surface is sufficiently convex, depending only on…

In this paper, we study the hydrostatic approximation for the Navier-Stokes system in a thin domain. When the convex initial data with Gevrey regularity of optimal index 3/2 in x variable and Sobolev regularity in y variable, we justify the…

We study the hyperbolic version of the Prandtl system derived from the hyperbolic Navier-Stokes system with no-slip boundary condition. Compared to the classical Prandtl system, the quasi-linear terms in the hyperbolic Prandtl equation…

Stability of inviscid shear shallow water flows with free surface is studied in the framework of the Benney equations. This is done by investigating the generalized hyperbolicity of the integrodifferential Benney system of equations. It is…

A result of Gevrey regularity is ascertained for a semigroup which models a fluid-structure interaction problem. In this model, the fluid evolves in a piecewise smooth or convex geometry $\mathcal{O}$. On a portion of the boundary, a fourth…

We derive constraints on the existence of walls for Bridgeland stability conditions for general projective surfaces. We show that in suitable planes of stability conditions the walls are bounded and derive conditions for when the number of…

This paper deals with the optimal streaky perturbations (which maximize the perturbed energy growth) in a wedge flow boundary layer. These three dimensional perturbations are governed by a system of linearized boundary layer equations…

In $1904$, Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of incompressible Navier Stokes equations near a boundary as the viscosity goes to $0$. His Ansatz was that the solution of Navier Stokes…

We combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions. We analyze the behavior of facets at the parts of the boundary where these conditions are imposed. We devote…

The linear stability of buoyant parallel flow in a vertical porous layer with an annular cross-section is investigated. The vertical cylindrical boundaries are kept at different uniform temperatures and they are assumed to be impermeable.…

The {\L}ojasiewicz inequality characterizes objective-value convergence along gradient flows and, in special cases, yields exponential decay of the cost. However, such results do not directly give rates of convergence in the state. In this…

In this paper we use the notion of stability for free boundary surfaces with constant higher order mean curvature to obtain rigidity results for $H_2$-surfaces with free boundary of a geodesic ball of a simply connected $3$-dimensional…

We present a simple model for the development of shear layers between parallel flows in confining channels. Such flows are important across a wide range of topics from diffusers, nozzles and ducts to urban air flow and geophysical fluid…

We compute fully local boundary layer scales in three-dimensional turbulent Rayleigh-Benard convection. These scales are directly connected to the highly intermittent fluctuations of the fluxes of momentum and heat at the isothermal top and…