The form of the viscous term is discussed for incompressible flow on a two-dimensional curved surface S and for the shallow water equations. In the case of flow on a surface three versions are ...

1. Introduction The first derivations of the Navier-Stokes equation appeared in two memoirs by Claude-Louis Navier (1785-1836): Sur les lois des mouvements des fluides, en ayant égard à l'adhésion des ...

Abstract In this paper, the boundary layer equations (abbreviation BLE) for exterior flow around an obstacle are established using semi-geodesic coordinate system (S-coordinate) based on the curved ...

We provide the Burgers equation, Darcy flow, and Navier-Stokes equation datasets we used in the paper. The data generation configuration can be found in the paper. PDE datasets The datasets are given ...

Optimal orders of convergence for the Fourier-Galerkin method for two-dimensional Navier-Stokes equations in various energy norms and in Lp-norms of the velocity field are proved. Optimal orders of ...

Navier-Stokes Equations: Fundamental equations governing the motion of viscous fluid substances. Q-tensor: A mathematical representation of the local orientational order in nematic liquid crystals.