About Steady Transport Equation II - Schauder Estimates in Domains with Smooth Boundaries

Antonin Novotny

Abstract: This paper is a continuation of our work [7]. 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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