Abstract
The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier–Stokes system (N). This description corresponds to the so-called Eulerian approach. We develop a new approximation method for (N) in both the steady and the nonsteady 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, which contains a convergent subsequence with limit function v such that v is a weak solution on (N).
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Varnhorn, W. (2018). Steady and Unsteady Navier–Stokes Flow with Lagrangian Differences. In: Pinelas, S., Caraballo, T., Kloeden, P., Graef, J. (eds) Differential and Difference Equations with Applications. ICDDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 230. Springer, Cham. https://doi.org/10.1007/978-3-319-75647-9_43
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DOI: https://doi.org/10.1007/978-3-319-75647-9_43
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