# Lagrangian approximations and weak solutions of the Navier-Stokes equations

Banach Center Publications (2008)

- Volume: 81, Issue: 1, page 515-532
- ISSN: 0137-6934

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topWerner Varnhorn. "Lagrangian approximations and weak solutions of the Navier-Stokes equations." Banach Center Publications 81.1 (2008): 515-532. <http://eudml.org/doc/281866>.

@article{WernerVarnhorn2008,

abstract = {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.},

author = {Werner Varnhorn},

journal = {Banach Center Publications},

keywords = {Navier-Stokes equation; Lagrangian approximation; weak solution},

language = {eng},

number = {1},

pages = {515-532},

title = {Lagrangian approximations and weak solutions of the Navier-Stokes equations},

url = {http://eudml.org/doc/281866},

volume = {81},

year = {2008},

}

TY - JOUR

AU - Werner Varnhorn

TI - Lagrangian approximations and weak solutions of the Navier-Stokes equations

JO - Banach Center Publications

PY - 2008

VL - 81

IS - 1

SP - 515

EP - 532

AB - 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.

LA - eng

KW - Navier-Stokes equation; Lagrangian approximation; weak solution

UR - http://eudml.org/doc/281866

ER -

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