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The Navier-Stokes Equations with Particle Methods

Varnhorn, Werner

The non-stationary nonlinear Navier-Stokes equations describe the motion of a viscous incompressible fluid flow for 0<t≤T in some bounded three-dimensional domain. Up to now it is not known wether these equations are well-posed or not. Therefore we use a particle method to develop a system of approximate equations. We show that this system can be solved uniquely and globally in time and that its solution has a high degree of spatial regularity. Moreover we prove that the system of approximate solutions has an accumulation point satisfying the Navier-Stokes equations in a weak sense.

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Citation
In: Mathematische Schriften Kassel 07, 04 / (2007) , S. ; 
@article{urn:nbn:de:hebis:34-2008022020404,
  author    ={Varnhorn, Werner},
  title    ={The Navier-Stokes Equations with Particle Methods},
  copyright  ={https://rightsstatements.org/page/InC/1.0/},
  language ={en},
  year   ={2007}
}