Abstract.
It is shown that Poisson-like equations for 3-vector fields can have divergence-free solutions and desired boundary behaviour in bounded domains, provided the mean curvature of the boundary is nowhere too large positive. A-priori estimates for the solutions are given.
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Sauer, N. Divergence-Free Solutions of Poisson-Like Equations. J. math. fluid mech. 7, 405–412 (2005). https://doi.org/10.1007/s00021-004-0122-x
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DOI: https://doi.org/10.1007/s00021-004-0122-x