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 ...

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 ...

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 ...

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.