# About steady transport equation I – ${L}^{p}$-approach in domains with smooth boundaries

Commentationes Mathematicae Universitatis Carolinae (1996)

- Volume: 37, Issue: 1, page 43-89
- ISSN: 0010-2628

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topNovotný, Antonín. "About steady transport equation I – $L^p$-approach in domains with smooth boundaries." Commentationes Mathematicae Universitatis Carolinae 37.1 (1996): 43-89. <http://eudml.org/doc/247942>.

@article{Novotný1996,

abstract = {We investigate the steady transport equation \[ \lambda z+w\cdot \nabla z+az=f,\quad \lambda >0 \]
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 particular 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 presented here is well adapted for applications in various problems of compressible fluid dynamics.},

author = {Novotný, Antonín},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {steady transport equation; bounded; unbounded; exterior domains; existence of solutions; estimates; steady transport equation; bounded, unbounded, exterior domains; existence of solutions},

language = {eng},

number = {1},

pages = {43-89},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {About steady transport equation I – $L^p$-approach in domains with smooth boundaries},

url = {http://eudml.org/doc/247942},

volume = {37},

year = {1996},

}

TY - JOUR

AU - Novotný, Antonín

TI - About steady transport equation I – $L^p$-approach in domains with smooth boundaries

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1996

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 37

IS - 1

SP - 43

EP - 89

AB - We investigate the steady transport equation \[ \lambda z+w\cdot \nabla z+az=f,\quad \lambda >0 \]
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 particular 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 presented here is well adapted for applications in various problems of compressible fluid dynamics.

LA - eng

KW - steady transport equation; bounded; unbounded; exterior domains; existence of solutions; estimates; steady transport equation; bounded, unbounded, exterior domains; existence of solutions

UR - http://eudml.org/doc/247942

ER -

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