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

Antonín Novotný

Commentationes Mathematicae Universitatis Carolinae (1996)

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

Abstract

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We investigate the steady transport equation λ z + w · z + a z = 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 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.

How to cite

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Novotný, 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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