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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.
Werner 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 -