“Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means. But we have proved it, and therefore we know it must be the truth.” —Benjamin ...

The compressible Euler equations form the cornerstone of fluid dynamics, describing the conservation of mass, momentum and energy in a compressible fluid. When augmented by damping effects, these ...

The Euler and Navier-Stokes equations form the cornerstone of fluid dynamics, governing the motion of fluids under a wide range of conditions. The Euler equations describe inviscid flows where ...

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the ...

In this note, we rigorously justify a singular approximation of the incompressible Navier-Stokes equations. Our approximation combines two classical approximations of the incompressible Euler ...