Search

Summary

There are two great equations of classical physics: one is Einstein’s equation of general relativity, the other the Navier-Stokes equation that describes how fluids flow. In this chapter, we meet Navier-Stokes.

This equation differs from the Euler equation by the addition of a viscosity term. This is not a small change and makes solutions to the Navier-Stokes equation much richer and more subtle than those of the Euler equation. In this chapter, we begin our exploration of these solutions.

Summary

This contribution covers the topic of my talk at the 2016-17 Warwick-EPSRC Symposium: 'PDEs and their applications'. As such it contains some already classical material and some new observations. The main purpose is to compare several avatars of the Kato criterion for the convergence of a Navier-Stokes solution, to a regular solution of the Euler equations, with numerical or physical issues like the presence (or absence) of anomalous energy dissipation, the Kolmogorov 1/3 law or the Onsager C^{0,1/3} conjecture. Comparison with results obtained after September 2016 and an extended list of references have also been added.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

2 - The Navier–Stokes Equation

Summary

1 - Remarks on recent advances concerning boundary effects and the vanishing viscosity limit of the Navier–Stokes equations

Summary

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

2 - The Navier–Stokes Equation

Summary

1 - Remarks on recent advances concerning boundary effects and the vanishing viscosity limit of the Navier–Stokes equations

Summary