Lagrangian approximations and weak solutions of the Navier-Stokes equations

Tom 81 / 2008

Werner Varnhorn Banach Center Publications 81 (2008), 515-532 MSC: Primary 35B65; Secondary 67D05. DOI: 10.4064/bc81-0-33

Streszczenie

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.

Autorzy

  • Werner VarnhornFaculty of Mathematics
    University of Kassel
    Heinrich-Plett-Str. 40
    34132 Kassel, Germany
    e-mail

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