A pseudo-differential treatment of general inhomogeneous initial-boundary value problems for the Navier-Stokes equation
Grubb, Gerd ; Solonnikov, Vsevolod A.
Journées équations aux dérivées partielles, (1988), p. 1-8 / Harvested from Numdam
Publié le : 1988-01-01
@article{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},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {1988},
     pages = {1-8},
     mrnumber = {89m:35179},
     zbl = {0675.76028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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), pp. 1-8. http://gdmltest.u-ga.fr/item/JEDP_1988____A3_0/

[BM]. L. Boutet De Monvel, Boundary problems for pseudo-differential operators, Acta Mat. 126 (1971), 11-51. | MR 53 #11674 | Zbl 0206.39401

[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 57 #919 | Zbl 0386.35037

[Fu-K]. H. Fujita and T. Kato, On the Navier-Stokes initial value problem I, Arch. Rat. Mech. Anal. 16 (1964), 269-315. | MR 29 #3774 | Zbl 0126.42301

[Gi 1]. Y. Giga, Analyticity of the semigroup generated by the Stokes operator in Lr-spaces, Math. Zeitschr. 178 (1981), 297-329. | MR 83e:47028 | Zbl 0473.35064

[Gi 2]. Y. Giga, The nonstationary Navier-Stokes system with some first order boundary conditions, Proc. Jap. Acad. 58 (1982), 101-104. | MR 83j:35131 | Zbl 0524.35086

[Gi 3]. Y. Giga, Domains of fractional powers of the Stokes operator in Lr spaces, Arch. Rat. Mech. Anal. 89 (1985), 251-265. | MR 86m:47074 | Zbl 0584.76037

[Gi 4]. Y. Giga, Weak and strong solutions of the Navier-Stokes initial value problem, Publ. RIMS, Kyoto Univ. 19 (1983), 887-910. | MR 85j:35157 | Zbl 0547.35101

[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 86m:35138 | Zbl 0587.35078

[Gr]. G. Grubb, “Functional calculus of pseudo-differential boundary problems”, Birkhäuser, Boston, 1986. | MR 88f:35002 | Zbl 0622.35001

[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 89c:35131 | Zbl 0655.35065

[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 82c:35067 | Zbl 0455.35099

[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 85k:35192 | Zbl 0548.35096

[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 0092.43104

[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. | MR 30 #2240 | Zbl 0163.33901

[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 54 #3188 | Zbl 0404.35081

[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 0429.76020

[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. | Zbl 0585.76039

[Te]. R. Temam, “Navier-Stokes Equations”, North-Holland, Amsterdam, 1977. | Zbl 0383.35057