In this Note, we prove the existence of a partially strong solution to the steady Navier–Stokes equations for viscous barotropic compressible fluids, in a bounded simply connected domain of with the prescribed generalized impermeability conditions , on the boundary. We call the solution “partially strong” because only the divergence-free part of the velocity field and the associated effective pressure have regularity typical for strong solution, while the density and the gradient part of the velocity have regularity typical for weak solution.
Dans cette Note, nous démontrons l'existence de solutions partiellement fortes pour les équations de Navier–Stokes stationnaires descriptives de fluides visqueux barotropiques compressibles, dans un domaine borné de , avec des conditions aux limites d'imperméabilité généralisée , . Nous utilisons le libellé « solution partiellement forte » pour dire que les propriétés de régularité de la partie à divergence nulle du champ des vitesses et de la pression effective associée sont typiques d'une solution forte, tandis que les propriétés de régularité de la densité et de la partie complémentaire du champ des vitesses (gradient d'un potentiel) sont typiques d'une solution faible.
Accepted:
Published online:
Olivier Muzereau 1; Jiří Neustupa 2; Patrick Penel 1
@article{CRMATH_2010__348_11-12_619_0, author = {Olivier Muzereau and Ji\v{r}{\'\i} Neustupa and Patrick Penel}, title = {A steady {Navier{\textendash}Stokes} model for compressible fluid with partially strong solutions}, journal = {Comptes Rendus. Math\'ematique}, pages = {619--624}, publisher = {Elsevier}, volume = {348}, number = {11-12}, year = {2010}, doi = {10.1016/j.crma.2010.04.001}, language = {en}, }
TY - JOUR AU - Olivier Muzereau AU - Jiří Neustupa AU - Patrick Penel TI - A steady Navier–Stokes model for compressible fluid with partially strong solutions JO - Comptes Rendus. Mathématique PY - 2010 SP - 619 EP - 624 VL - 348 IS - 11-12 PB - Elsevier DO - 10.1016/j.crma.2010.04.001 LA - en ID - CRMATH_2010__348_11-12_619_0 ER -
%0 Journal Article %A Olivier Muzereau %A Jiří Neustupa %A Patrick Penel %T A steady Navier–Stokes model for compressible fluid with partially strong solutions %J Comptes Rendus. Mathématique %D 2010 %P 619-624 %V 348 %N 11-12 %I Elsevier %R 10.1016/j.crma.2010.04.001 %G en %F CRMATH_2010__348_11-12_619_0
Olivier Muzereau; Jiří Neustupa; Patrick Penel. A steady Navier–Stokes model for compressible fluid with partially strong solutions. Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 619-624. doi : 10.1016/j.crma.2010.04.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.04.001/
[1] On the Navier–Stokes equation with boundary conditions based on vorticity, Math. Nachr., Volume 269–270 (2004), pp. 59-72
[2] J. Frehse, M. Steinhauer, V. Weigant, The Dirichlet problem for steady viscous flow in 3-D, Preprint No. 347, Univ. Bonn, 2007
[3] Mathematical Topics in Fluid Mechanics, Compressible Models, Oxford University Press 2, 1998
[4] 3D steady compressible Navier–Stokes equations, Discr. Cont. Dyn. Systems, Ser. S, Volume 1 (2008) no. 1, pp. 151-163
[5] O. Muzereau, Weak solutions to steady compressible Navier–Stokes equations with vorticity type boundary conditions, Dissertation thesis, Univ. Sud Toulon–Var, 2009
[6] O. Muzereau, J. Neustupa, P. Penel, A weak solvability to the steady Navier–Stokes equations for compressible barotropic fluid with generalized impermeability boundary conditions, Applicable Analysis, in press
[7] O. Muzereau, J. Neustupa, P. Penel, A partially strong solution to the steady Navier–Stokes equations for compressible barotropic fluid with generalized impermeability boundary conditions, Preprint Univ. Sud Toulon-Var, 2009
[8] On regularity of a weak solution to the Navier–Stokes equations with generalized impermeability boundary conditions, J. Nonlinear Analysis, Volume 66 (2007), pp. 1753-1769
[9] Introduction to the Mathematical Theory of Compressible Flow, Oxford University Press 27, 2004
Cited by Sources:
Comments - Policy