A pseudo-differential treatment of general inhomogeneous initial-boundary value problems for the Navier-Stokes equation
Journées équations aux dérivées partielles (1988), article no. 3, 8 p. 
@incollection{JEDP_1988____A3_0,
     author = {Grubb, Gerd and Solonnikov, Vsevolod A.},
     title = {A pseudo-differential treatment of general inhomogeneous initial-boundary value problems for the {Navier-Stokes} equation},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {3},
     pages = {1--8},
     publisher = {Ecole polytechnique},
     year = {1988},
     mrnumber = {89m:35179},
     zbl = {0675.76028},
     language = {en},
     url = {http://archive.numdam.org/item/JEDP_1988____A3_0/}
}
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
SP  - 1
EP  - 8
PB  - Ecole polytechnique
UR  - http://archive.numdam.org/item/JEDP_1988____A3_0/
LA  - en
ID  - JEDP_1988____A3_0
ER  - 
%0 Journal Article
%A Grubb, Gerd
%A Solonnikov, Vsevolod A.
%T A pseudo-differential treatment of general inhomogeneous initial-boundary value problems for the Navier-Stokes equation
%J Journées équations aux dérivées partielles
%D 1988
%P 1-8
%I Ecole polytechnique
%U http://archive.numdam.org/item/JEDP_1988____A3_0/
%G en
%F JEDP_1988____A3_0
Grubb, Gerd; 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), article  no. 3, 8 p. http://archive.numdam.org/item/JEDP_1988____A3_0/

[BM]. L. Boutet De Monvel, Boundary problems for pseudo-differential operators, Acta Mat. 126 (1971), 11-51. | MR | Zbl

[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. | MR | Zbl

[Fu-K]. H. Fujita and T. Kato, On the Navier-Stokes initial value problem I, Arch. Rat. Mech. Anal. 16 (1964), 269-315. | MR | Zbl

[Gi 1]. Y. Giga, Analyticity of the semigroup generated by the Stokes operator in Lr-spaces, Math. Zeitschr. 178 (1981), 297-329. | MR | Zbl

[Gi 2]. Y. Giga, The nonstationary Navier-Stokes system with some first order boundary conditions, Proc. Jap. Acad. 58 (1982), 101-104. | MR | Zbl

[Gi 3]. Y. Giga, Domains of fractional powers of the Stokes operator in Lr spaces, Arch. Rat. Mech. Anal. 89 (1985), 251-265. | MR | Zbl

[Gi 4]. Y. Giga, Weak and strong solutions of the Navier-Stokes initial value problem, Publ. RIMS, Kyoto Univ. 19 (1983), 887-910. | MR | Zbl

[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. | MR | Zbl

[Gr]. G. Grubb, “Functional calculus of pseudo-differential boundary problems”, Birkhäuser, Boston, 1986. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[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. | Zbl

[Te]. R. Temam, “Navier-Stokes Equations”, North-Holland, Amsterdam, 1977. | Zbl