Vol. 54, No. 3, pp. 317-333 (1997)
About Steady Transport Equation II - Schauder Estimates in Domains with Smooth Boundaries
Antonin NovotnyDepartment of Mathematics, ETMA,
B.P. 132, 839 57 La Garde - FRANCE
Abstract: This paper is a continuation of our work . We investigate steady transport equation $$ \lambda\,z+w\cdot\nabla z+a\,z=f\nvirg \lambda>0, $$ in various domains (bounded or unbounded) with sufficiently smooth compact or noncompact boundaries. The coefficients $w$ and $a$ are ``sufficiently smooth functions, ``small in appropriate norms. There is no transport of $z$ through the boundary. Under these assumptions, we study existence, regularity, uniqueness and asymptotic behaviour (when the domain is unbounded) of solutions in spaces of Holder continuous functions. The corresponding estimates are derived. The results presented here have found a series of applications in the compressible fluid dynamics.
Classification (MSC2000): 35Q35, 35L, 76N
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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.