@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]. Boundary problems for pseudo-differential operators, Acta Mat. 126 (1971), 11-51. | MR 53 #11674 | Zbl 0206.39401
,[F-L-R]. Boundary value problems for the Navier-Stokes equations, Amer. J. Math. 99 (1977), 626-668. | MR 57 #919 | Zbl 0386.35037
, and ,[Fu-K]. On the Navier-Stokes initial value problem I, Arch. Rat. Mech. Anal. 16 (1964), 269-315. | MR 29 #3774 | Zbl 0126.42301
and ,[Gi 1]. 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]. 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]. 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]. 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]. Solutions in Lr of the Navier-Stokes initial value problem, Arch. Rat. Mech. Anal. 89 (1985), 267-281. | MR 86m:35138 | Zbl 0587.35078
and ,[Gr]. “Functional calculus of pseudo-differential boundary problems”, Birkhäuser, Boston, 1986. | MR 88f:35002 | Zbl 0622.35001
,[Gr-S]. 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
and ,[La]. “Mathematical problems of viscous incompressible flow”, “Nauka”, Moscow, 1970.
,[M]. 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]. 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]. “Hydrodynamik”, Akademische Verlagsgesellschaft M. B. H., Leipzig, 1927.
,[So]. On non-stationary equations of hydrodynamics for viscous fluid, Dokl. Akad. Nauk SSSR 128 (1959), 45-48. | Zbl 0092.43104
,[S 1]. 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]. 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]. 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]. 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]. “Navier-Stokes Equations”, North-Holland, Amsterdam, 1977. | Zbl 0383.35057
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