Schauder estimates for steady compressible Navier-Stokes equations in bounded domains
Rendiconti del Seminario Matematico della Università di Padova, Volume 98  (1997), p. 125-139
@article{RSMUP_1997__98__125_0,
     author = {Dutto, Patrick and Impagliazzo, Jean-Luc and Novotny, Antonin},
     title = {Schauder estimates for steady compressible Navier-Stokes equations in bounded domains},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {98},
     year = {1997},
     pages = {125-139},
     zbl = {0897.35062},
     mrnumber = {1492973},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1997__98__125_0}
}
Dutto, Patrick; Impagliazzo, Jean-Luc; Novotny, Antonin. Schauder estimates for steady compressible Navier-Stokes equations in bounded domains. Rendiconti del Seminario Matematico della Università di Padova, Volume 98 (1997) , pp. 125-139. http://www.numdam.org/item/RSMUP_1997__98__125_0/

[ADN] Agmon S. - Douglis A. - Nirenberg L., Estimates near the boundary of solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math., 17 (1964), pp. 35-92. | MR 162050 | Zbl 0123.28706

[BV1] Beirao Da Veiga H., An Lp theory for the n dimensional, stationary compressible Navier-Stokes equations and the incompressible limit for compressible fluids. The equilibrium solutions, Comm. Math. Phys., 109 (1987), pp. 229-248. | MR 880415 | Zbl 0621.76074

[BV2] Beirao Da Veiga H., Existence results in Sobolev spaces for a stationary transport equation, Ricerche di Matematica, Volume in honour of prof. C. Miranda (1987). | Zbl 0691.35087

[BV3] Beirao Da Veiga H., Boundary value problem for a class of first order partial differential equation in Sobolev spaces and application to the Euler flow, Rend. Sem. Mat. Univ. Padova, 79 (1987), pp. 247-273. | Numdam | MR 964034 | Zbl 0709.35082

[C] Cattabriga L., Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Sem. Mat. Univ. Padova, 31 (1961), pp. 308-340. | Numdam | MR 138894 | Zbl 0116.18002

[G1] Galdi G.P., An introduction to the mathematical theory of the Navier-Stokes equations. Vol I: Linearized stationary problems, Springer Tracts in Natural Philosophy, 38 (1994). | MR 1284205 | Zbl 0949.35004

[No1] Novotny A., About the steady transport equation I, Lp approach in domains with smooth boundaries, Comm. Mat. Univ. Carolinae, 37, 1 (1996), pp. 43-89. | MR 1396161 | Zbl 0852.35115

[No2] Novotny A., About the steady transport equation II, Schauder estimates in domains with smooth boundaries (1993), to appear. | MR 1472165 | Zbl 0893.35105

[NP1] Novotny A. - Padula M., Lp approach to steady flows of viscous compressible fluids in exterior domains, Arch. Rat. Mech. Anal., 126 (1994), pp. 243-297. | MR 1293786 | Zbl 0809.76080

[NP2] Novotny A. - Padula M., Existence and uniqueness of stationary solutions for viscous compressible heat conductive fluid with large potential and small nonpotential external forces, Sib. Math. J., 34 (1993), pp. 120-146. | MR 1255466 | Zbl 0808.76083

[NoPe] Novotny A. - Penel P., Lp approach to steady flows of viscous heat conductive fluids on exterior domains, I, II, M3 AS (1994) (in the press).

[Os] Osmolovskii V., The free surface of a drop in a symmetric force field, Zapiski Nauchn. Sem. LOMI, 52 (1975), pp. 160-174 (in Russian). | MR 446063 | Zbl 0358.76026

[P1] Padula M., Existence and uniqueness for viscous steady compressible motions, Arch. Rat. Mech. Anal., 77 (1987), pp. 89-102. | MR 860302 | Zbl 0644.76086

[SiSo1] Simader Ch. - Sohr H., The weak dirichlet problem for Δ in Lq in bounded and exterior domains, Stab. Anal. Cont. Media, 2 (1992), pp. 183-202.

[So1] Solonnikov V.A., On a free boundary problem for the system of Navier-Stokes equations, Trudy Sem. S. L. Sobolev, 2 (1978), pp. 127-140 (in Russian). | MR 568037 | Zbl 0422.76020

[So2] Solonnikov V.A., On the Stokes equation in domains with non smooth boundaries and on a viscous incompressible flow with a free surface, Nonlin. Part. Diff. Eq., 3, Collège de France Seminar (1980- 1981), pp. 340-423. | MR 670285 | Zbl 0506.35083

[So3] Solonnikov V.A., Some free boundary problems for the Navier-Stokes equations with moving contact points and lines (1995), Preprint. | MR 1343648 | Zbl 0926.35116

[V1] Valli A., On the existence of stationary solutions to compressible Navier-Stokes equations, Ann. Inst. H. Poincaré, 4 (1987), pp. 99-113. | Numdam | MR 877992 | Zbl 0627.76080

[V2] Valli A., Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method, Ann. Sc. Norm. Sup. Pisa, 4 (1983), pp. 607-647. | Numdam | MR 753158 | Zbl 0542.35062