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Anton´ın Novotn´ y

About steady transport equation I |

Lp

-approach in domains with smooth boundaries

Comment.Math.Univ.Carolinae 37,1 (1996) 41-87.

Abstract: We investigate the steady transport equation λz+w· ∇z+az=f, λ >0

in various domains (bounded or unbounded) with smooth noncompact boundaries.

The functions w, a are supposed to be small in appropriate norms. The solution is studied in spaces of Sobolev type (classical Sobolev spaces, Sobolev spaces with weights, homogeneous Sobolev spaces, dual spaces to Sobolev spaces). The partic- ular stress is put onto the problem to extend the results to as less regular vector fields w, a, as possible (conserving the requirement of smallness). The theory pre- sented here is well adapted for applications in various problems of compressible fluid dynamics.

Keywords: steady transport equation, bounded, unbounded, exterior domains, existence of solutions, estimates

AMS Subject Classification: 35Q35, 35L, 76N

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