Asymptotic Analysis of Fluid Equations

Abstract

Nonlinear partial differential equations describing the fluid motion make a long list, most of which date back to the 19th century or earlier. Among them are the Boltzmann equation, the Navier-Stokes and Euler equations, compressible and incompressible, to mention a few. The Newton equation should be also included in the list as a microscopic fluid equation which consider the fluid to be a many-particle system. On the other hand, the Navier-Stokes and Euler equations are macroscopic fluid equations regarding the fluid as a continuum, and the Boltzmann equation is in-between.