Abstract
We give a simple approach to the theory of the steady transport equation, providing some results that are needed in the theory of steady compressible viscous flow. In particular, we prove the assertions that are collected together in Lemma 3 of our accompanying paper [11]. Our methods are based on a construction of solutions by Galerkin approximation and on duality arguments with the adjoint equation. We conclude with some heuristic observations based on the theory of characteristics, explaining, particularly, the need for successively stronger restrictions on the size of the velocity field, in order to prove successively more regularity of the solution.
This work has been supported by the Natural Sciences and Engineering Research Council of Canada, contracts MURST and the GNFM of Italian CNR, and the Deutsche Forschungsgemeinschaft.
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Heywood, J.G., Padula, M. (2000). On The Steady Transport Equation. In: Galdi, G.P., Heywood, J.G., Rannacher, R. (eds) Fundamental Directions in Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8424-2_4
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DOI: https://doi.org/10.1007/978-3-0348-8424-2_4
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