A pseudo-differential treatment of general inhomogeneous initial-boundary value problems for the Navier-Stokes equation
Gerd Grubb; Vsevolod A. Solonnikov
Journées équations aux dérivées partielles (1988)
- page 1-8
- ISSN: 0752-0360
Access Full Article
topHow to cite
topGrubb, Gerd, and Solonnikov, Vsevolod A.. "A pseudo-differential treatment of general inhomogeneous initial-boundary value problems for the Navier-Stokes equation." Journées équations aux dérivées partielles (1988): 1-8. <http://eudml.org/doc/93176>.
@article{Grubb1988,
author = {Grubb, Gerd, Solonnikov, Vsevolod A.},
journal = {Journées équations aux dérivées partielles},
keywords = {Navier-Stokes equations; mixed non-homogeneous boundary conditions; Neumann type boundary data; degenerate parabolic; pseudo-differential operators; convective terms; compatibility condition},
language = {eng},
pages = {1-8},
publisher = {Ecole polytechnique},
title = {A pseudo-differential treatment of general inhomogeneous initial-boundary value problems for the Navier-Stokes equation},
url = {http://eudml.org/doc/93176},
year = {1988},
}
TY - JOUR
AU - Grubb, Gerd
AU - Solonnikov, Vsevolod A.
TI - A pseudo-differential treatment of general inhomogeneous initial-boundary value problems for the Navier-Stokes equation
JO - Journées équations aux dérivées partielles
PY - 1988
PB - Ecole polytechnique
SP - 1
EP - 8
LA - eng
KW - Navier-Stokes equations; mixed non-homogeneous boundary conditions; Neumann type boundary data; degenerate parabolic; pseudo-differential operators; convective terms; compatibility condition
UR - http://eudml.org/doc/93176
ER -
References
top- [BM]. L. BOUTET DE MONVEL, Boundary problems for pseudo-differential operators, Acta Mat. 126 (1971), 11-51. Zbl0206.39401MR53 #11674
- [F-L-R]. E. B. FABES, J. E. LEWIS and N. M. RIVIERE, Boundary value problems for the Navier-Stokes equations, Amer. J. Math. 99 (1977), 626-668. Zbl0386.35037MR57 #919
- [Fu-K]. H. FUJITA and T. KATO, On the Navier-Stokes initial value problem I, Arch. Rat. Mech. Anal. 16 (1964), 269-315. Zbl0126.42301MR29 #3774
- [Gi 1]. Y. GIGA, Analyticity of the semigroup generated by the Stokes operator in Lr-spaces, Math. Zeitschr. 178 (1981), 297-329. Zbl0473.35064MR83e:47028
- [Gi 2]. Y. GIGA, The nonstationary Navier-Stokes system with some first order boundary conditions, Proc. Jap. Acad. 58 (1982), 101-104. Zbl0524.35086MR83j:35131
- [Gi 3]. Y. GIGA, Domains of fractional powers of the Stokes operator in Lr spaces, Arch. Rat. Mech. Anal. 89 (1985), 251-265. Zbl0584.76037MR86m:47074
- [Gi 4]. Y. GIGA, Weak and strong solutions of the Navier-Stokes initial value problem, Publ. RIMS, Kyoto Univ. 19 (1983), 887-910. Zbl0547.35101MR85j:35157
- [Gi-M]. Y. GIGA and T. MIYAKAWA, Solutions in Lr of the Navier-Stokes initial value problem, Arch. Rat. Mech. Anal. 89 (1985), 267-281. Zbl0587.35078MR86m:35138
- [Gr]. G. GRUBB, “Functional calculus of pseudo-differential boundary problems”, Birkhäuser, Boston, 1986. Zbl0622.35001MR88f:35002
- [Gr-S]. G. GRUBB and V. A. Solonnikov, Reduction of basic initial-boundary value problems for the Stokes equation to initial-boundary value problems for systems of pseudodifferential equations, Zap. Nauchn. Sem. L.O.M.I. 163 (1987), 37-48 ; Transl. in Copenh. Univ. Math. Dept. Report Ser. 1987 no. 2. Zbl0655.35065MR89c:35131
- [La]. O. A. LADYZHENSKAYA, “Mathematical problems of viscous incompressible flow”, “Nauka”, Moscow, 1970.
- [M]. T. MIYAKAWA, The Lp approach to the Navier-Stokes equations with the Neumann boundary condition, Hiroshima Math. J. 10 (1980), 517-537. Zbl0455.35099MR82c:35067
- [Mo]. I. SH. MOGILEVSKIĬ, Estimates for solutions of a general initial-boundary value problem for the linear nonstationary system of Navier-Stokes equations in a bounded domain, Proc. Math. Inst. Steklov 159 (1982), 61-94. Zbl0548.35096MR85k:35192
- [Os]. C. W. OSEEN, “Hydrodynamik”, Akademische Verlagsgesellschaft M. B. H., Leipzig, 1927.
- [So]. P. E. SOB OLEVSKIĬ, On non-stationary equations of hydrodynamics for viscous fluid, Dokl. Akad. Nauk SSSR 128 (1959), 45-48. Zbl0092.43104
- [S 1]. V. A. SOLONNIKOV, On differentiability properties of solutions of the first boundary value problem for nonstationary system of Navier-Stokes equations, Proc. Mat. Inst. Steklov 73 (1964), 221-291. Zbl0163.33901MR30 #2240
- [S 2]. V. A. SOLONNIKOV, Estimates for solutions of nonstationary Navier-Stokes systems, Zap. Nauchn. Sem. LOMI 38 (1973), 153-231 ; English transl., J. Soviet Math. 8 (1977), 467-529. Zbl0404.35081MR54 #3188
- [S 3]. V. A. SOLONNIKOV, Solvability of a problem on the plane motion of a heavy viscous incompressible capillary liquid partially filling a container, Izv. Akad. Nauk SSSR 43 (1979) ; Math. USSR Izvestija 14 (1980), 193-221. Zbl0429.76020
- [S 4]. V. A. SOLONNIKOV, Solvability of the problem of evolution of an isolated volume of viscous, incompressible capillary fluid, Zap. Nauchn. Sem. L.O.M.I. 140 (1984), 179-186 ; J. Soviet Math. 32 (1986), 223-228. Zbl0585.76039
- [Te]. R. TEMAM, “Navier-Stokes Equations”, North-Holland, Amsterdam, 1977. Zbl0383.35057
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.