A Regularity Result for a Solid-Fluid System Associated to the Compressible Navier-Stokes Equations
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 3, p. 777-813
@article{AIHPC_2009__26_3_777_0,
author = {Boulakia, M. and Guerrero, S.},
title = {A Regularity Result for a Solid-Fluid System Associated to the Compressible Navier-Stokes Equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {26},
number = {3},
year = {2009},
pages = {777-813},
doi = {10.1016/j.anihpc.2008.02.004},
zbl = {1177.35146},
mrnumber = {2526402},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2009__26_3_777_0}
}

Boulakia, M.; Guerrero, S. A Regularity Result for a Solid-Fluid System Associated to the Compressible Navier-Stokes Equations. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 3, pp. 777-813. doi : 10.1016/j.anihpc.2008.02.004. http://www.numdam.org/item/AIHPC_2009__26_3_777_0/

[1] Beirão Da Veiga H., On the Existence of Strong Solutions to a Coupled Fluid-Structure Evolution Problem, J. Math. Fluid Mech. 6 (1) (2004) 21-52. | MR 2027753 | Zbl 1068.35087

[2] Boulakia M., Existence of Weak Solutions for an Interaction Problem Between an Elastic Structure and a Compressible Viscous Fluid, J. Math. Pures Appl. 84 (11) (2005) 1515-1554. | MR 2181459 | Zbl 1159.35395

[3] Boulakia M., Existence of Weak Solutions for the Three Dimensional Motion of an Elastic Structure in an Incompressible Fluid, J. Math. Fluid Mech. 9 (2) (2007) 262-294. | MR 2329269 | Zbl 1171.74337

[4] Chambolle A., Desjardins B., Esteban M. J., Grandmont C., Existence of Weak Solutions for the Unsteady Interaction of a Viscous Fluid With an Elastic Plate, J. Math. Fluid Mech. 7 (3) (2005) 368-404. | MR 2166981 | Zbl 1080.74024

[5] Conca C., San Martin J., Tucsnak M., Existence of Solutions for the Equations Modelling the Motion of a Rigid Body in a Viscous Fluid, Comm. Partial Differential Equations 25 (5-6) (2000) 1019-1042. | MR 1759801 | Zbl 0954.35135

[6] Coutand D., Shkoller S., Motion of an Elastic Solid Inside an Incompressible Viscous Fluid, Arch. Ration. Mech. Anal. 176 (1) (2005) 25-102. | MR 2185858 | Zbl 1064.74057

[7] Desjardins B., Esteban M. J., On Weak Solutions for Fluid-Rigid Structure Interaction: Compressible and Incompressible Models, Comm. Partial Differential Equations 25 (7-8) (2000) 1399-1413. | MR 1765138 | Zbl 0953.35118

[8] Desjardins B., Esteban M. J., Grandmont C., Le Tallec P., Weak Solutions for a Fluid-Elastic Structure Interaction Model, Rev. Mat. Complut. 14 (2) (2001) 523-538. | MR 1871311 | Zbl 1007.35055

[9] Feireisl E., Novotný A., Petzeltová H., On the Existence of Globally Defined Weak Solutions to the Navier-Stokes Equations, J. Math. Fluid Mech. 3 (4) (2001) 358-392. | MR 1867887 | Zbl 0997.35043

[10] Feireisl E., On the Motion of Rigid Bodies in a Viscous Compressible Fluid, Arch. Ration. Mech. Anal. 167 (4) (2003) 281-308. | MR 1981859 | Zbl 1090.76061

[11] Feireisl E., Dynamics of Viscous Compressible Fluids, Oxford Science Publications, Oxford, 2004. | MR 2040667 | Zbl 1080.76001

[12] Grandmont C., Maday Y., Existence for an Unsteady Fluid-Structure Interaction Problem, M2AN Math. Model. Numer. Anal. 34 (3) (2000) 609-636. | Numdam | MR 1763528 | Zbl 0969.76017

[13] Hoff D., Global Solutions of the Navier-Stokes Equations for Multidimensional Compressible Flow With Discontinuous Initial Data, J. Differential Equations 120 (1) (1995) 215-254. | MR 1339675 | Zbl 0836.35120

[14] Hoff D., Strong Convergence to Global Solutions for Multidimensional Flows of Compressible, Viscous Fluids With Polytropic Equations of State and Discontinuous Initial Data, Arch. Ration. Mech. Anal. 132 (1) (1995) 1-14. | MR 1360077 | Zbl 0836.76082

[15] Lions P.-L., Existence Globale De Solutions Pour Les Équations De Navier-Stokes Compressibles Isentropiques, C. R. Acad. Sci. Paris Sér. I Math. 316 (12) (1993) 1335-1340. | MR 1226126 | Zbl 0778.76086

[16] Lions P. L., Mathematical Topics in Fluid Mechanics, Oxford Science Publications, Oxford, 1996. | Zbl 0866.76002

[17] Matsumura A., Nishida T., The Initial Value Problem for the Equations of Motion of Viscous and Heat-Conductive Gases, J. Math. Kyoto Univ. 20 (1) (1980) 67-104. | MR 564670 | Zbl 0429.76040

[18] Matsumura A., Nishida T., Initial-Boundary Value Problems for the Equations of Motion of General Fluids, in: Computing Methods in Applied Sciences and Engineering, V, Versailles, 1981, North-Holland, Amsterdam, 1982, pp. 389-406. | MR 784652 | Zbl 0505.76083

[19] San Martin J., Starovoitov V., Tucsnak M., Global Weak Solutions for the Two Dimensional Motion of Several Rigid Bodies in an Incompressible Viscous Fluid, Arch. Ration. Mech. Anal. 161 (2) (2002) 93-112. | MR 1870954 | Zbl 1018.76012

[20] Takahashi T., Analysis of Strong Solutions for the Equations Modeling the Motion of a Rigid-Fluid System in a Bounded Domain, Adv. Differential Equations 8 (12) (2003) 1499-1532. | MR 2029294 | Zbl 1101.35356

[21] Tani A., On the First Initial-Boundary Value Problem of Compressible Viscous Fluid Motion, Publ. RIMS, Kyoto Univ. 13 (1977) 193-253. | Zbl 0366.35070

[22] Temam R., Navier-Stokes Equations. Theory and Numerical Analysis, Studies in Mathematics and its Applications, vol. 2, North-Holland Publishing Co., Amsterdam, 1977. | MR 609732 | Zbl 0383.35057

[23] Zeidler E., Nonlinear Functional Analysis and Its Applications. I. Fixed-Point Theorems, Translated from the German by Peter R. Wadsack, Springer-Verlag, New York, 1986. | MR 816732 | Zbl 0583.47050