Related papers: On a linear problem arising in dynamic boundaries
In previous work, we derived new energy and entropy stable open boundary conditions and implementation procedures for linear and nonlinear initial boundary value problems. These boundary procedures results in estimates bounded by external…
In this work, we analytically derive the exact closed dynamical equations for a liquid with short-ranged interactions in large spatial dimensions using the same statistical mechanics tools employed to analyze Brownian motion. Our derivation…
The impact of a wedge-shaped body on the free surface of a weightless inviscid incompressible liquid is considered. Both symmetrical and unsymmetrical entries at constant velocity are dealt with. The differential problem corresponds to the…
In this paper, we study weakly nonlinear boundary value problems on infinite intervals. For such problems, we provide criteria for the existence of solutions as well as a qualitative description of the behavior of solutions depending on a…
The no-slip boundary condition at a solid-liquid interface is at the center of our understanding of fluid mechanics. However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated. We…
It is well known that a boundary layer develops along an infinite plate under oscillatory motion in a Newtonian fluid. In this work, this oscillatory boundary layer theory is generalized to the case of linear viscoelastic(LVE) flow. We…
The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
We prove a local existence theorem for the free boundary problem for a relativistic fluid in a fixed spacetime. Our proof involves an a priori estimate which only requires control of derivatives tangential to the boundary, which holds also…
After a brief introduction to several variational problems in the study of shapes of thin thickness structures, we deal with variational problems on 2-dimensional surface in 3-dimensional Euclidian space by using exterior differential…
We discuss a methodology that could be gainfully exploited using easily measurable experimental quantities to ascertain if the ``no-slip" boundary condition is appropriate for the flows of fluids past a solid boundary.
We consider a free-boundary model for the ice-sheet interacting with an ocean. The model captures the coupling between a viscous geophysical fluid and an elastic interface through kinematic and dynamic boundary conditions that account for…
In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from [Lasiecka, Szulc, and Zochoswki, Nonl. Anal.: Real World Appl., 44, 2018]. An elastic body…
We prove that, in a two-dimensional strip, a steady flow of an ideal incompressible fluid with no stationary point and tangential boundary conditions is a shear flow. The same conclusion holds for a bounded steady flow in a half-plane. The…
When speaking of unsolved problems in physics, this is surprising at first glance to discuss the case of fluid mechanics. However, there are many deep open questions that come with the theory of fluid mechanics. In this paper, we discuss…
We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The…
The theory of turbulent Newtonian fluids turns out that the choice of the boundary condition is a relevant issue, since it can modify the behavior of the fluid by creating or avoiding a strong boundary layer. In this work we study…
We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the…
The isometric embedding problem is a fundamental problem in differential geometry. A longstanding problem is considered in this paper to characterize intrinsic metrics on a two-dimensional Riemannian manifold which can be realized as…
We study the behaviour near a boundary point a of any positive solution of a nonlinear elliptic equations with forcing term which vanishes on the boundary except at a. Our results are based upon a priori estimates for solutions and…