Well-Posedness of Evolutionary Navier-Stokes Equations with Forces of Low Regularity on Two-Dimensional Domains

Eduardo Casas; Karl Kunisch

Well-Posedness of Evolutionary Navier-Stokes Equations with Forces of Low Regularity on Two-Dimensional Domains

Analysis of PDEs 2021-11-23 v3 Optimization and Control

Authors: Eduardo Casas , Karl Kunisch

Abstract

Existence and uniqueness of solutions to the Navier-Stokes equation in dimension two with forces in the space $L^q( (0,T); \mathbf{W}^{-1,p}(\Omega))$ for $p$ and $q$ in appropriate parameter ranges are proven. The case of spatially measured-valued inhomogeneities is included. For the associated Stokes equation the well-posedness results are verified in arbitrary dimensions with $1 < p, q < \infty$ arbitrary.

Keywords

navier-stokes equations well-posedness low regularity forces stokes equation two-dimensional domains measure-valued inhomogeneities

Cite

@article{arxiv.2004.10456,
  title  = {Well-Posedness of Evolutionary Navier-Stokes Equations with Forces of Low Regularity on Two-Dimensional Domains},
  author = {Eduardo Casas and Karl Kunisch},
  journal= {arXiv preprint arXiv:2004.10456},
  year   = {2021}
}

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