Lagrangian approximations and weak solutions of the Navier-Stokes equations

• Autorzy: Werner Varnhorn
• Języki publikacji: EN

Abstrakty

EN

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity containing a convergent subsequence with limit function v such that v is a weak solution of the Navier-Stokes equations.

Kategorie tematyczne

• 35B65: Smoothness and regularity of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 81
• Numer: 1
• Strony: 515-532

Daty

wydano

2008

Twórcy

autor

Werner Varnhorn

• Faculty of Mathematics, University of Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany

Identyfikatory

DOI

10.4064/bc81-0-33