Related papers: Boundary conditions for the Stokes problem and a p…

The existence and uniqueness of a solution to a generalized Blasius equation with asymptotic boundary conditions are proved. A new numerical approximation method is proposed.

We revisit stress problems in linear elasticity to provide a perspective from the geometrical and functionalanalytic points of view. For the static stress problem of linear elasticity with mixed boundary conditions we write the associated…

We consider the compressible (barotropic) Navier-Stokes system on time-dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behaviour, viscosity, and the pressure in the weak…

An approximate solution to the two dimensional Navier Stokes equation with periodic boundary conditions is obtained by representing the x any y components of fluid velocity with complex Fourier basis vectors. The chosen space of basis…

In this paper, we introduce a nonlocal model for linear steady Stokes system with physical no-slip boundary condition. We use the idea of volume constraint to enforce the no-slip boundary condition and prove that the nonlocal model is…

We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes…

Consider the stationary Boltzmann equation in 2D convex domains with diffusive boundary condition. In this paper, we establish the hydrodynamic limits while the boundary layers are present, and derive the steady Navier-Stokes-Fourier system…

Recently it has been shown that imposing Petrov type I condition on the boundary may reduce the Einstein's equation to the Navier-Stokes equation in the non-relativistic and near-horizon limit. In this paper we extend this framework to a…

A rigorous way to obtain sharp bounds for Stokes constants is introduced and illustrated on a concrete problem arising in applications.

Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…

We consider the Stokes system in the half-space with localized boundary data. We prove that a boundary layer separation point exists provided that a certain singular integral determined by the boundary data is negative. On the other hand,…

We prove Wolf's regularity condition up to the boundary for solutions to the Navier-Stokes equations satisfying non-slip boundary condition.

Boundary value problems for the nonlinear Schrodinger equation on the half line in laboratory coordinates are considered. A class of boundary conditions that lead to linearizable problems is identified by introducing appropriate extensions…

We present a novel approach to the Liouville problem for the stationary Navier-Stokes equations. As an application of our method, we prove conditional Liouville theorems with assumptions on the antiderivative of the velocity that represent…

In this paper we consider, by means of a precise spectral analysis, the 3D Navier-Stokes equations endowed with Navier slip-with-friction boundary conditions. We study the problem in a very simple geometric situation as the region between…

We consider a boundary value problem for the parabolic Lam\'e type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consists of recovering a vector-function, satisfying the…

In this work, we present some new Carleman inequalities for Stokes and Oseen equations with non-homogeneous boundary conditions. These estimates lead to log type stability inequalities for the problem of recovering the solution of the…

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…

We study the stepwise sine-Gordon equation, in which the system parameter is different for positive and negative values of the scalar field. By applying appropriate boundary conditions, we derive relations between the soliton velocities…

We prove the existence of a weak solution to the compressible Navier--Stokes system with singular pressure that explodes when density achieves its congestion level. This is a quantity whose initial value evolves according to the transport…