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On the interior approximate controllability for fractional wave equations
On some two phase problem for compressible and compressible viscous fluid flow separated by sharp interface
1. | Division of Mathematics, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki, 305-8571, Japan |
2. | Department of Mathematics and Research Institute of Science and Engineering, JST CREST, Waseda University, Ohkubo 3-4-1, Shinjuku-ku, Tokyo 169-8555 |
3. | Department of Mathematics, Faculty of Science and Technology, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama, 223-8522, Japan |
References:
[1] |
I. V. Denisova, Evolution of compressible and imcompressible fluids separated by a closed interface, Interface Free Bound., 2 (2000), 283-312.
doi: 10.4171/IFB/21. |
[2] |
I. V. Denisova and V. A. Solonnikov, Classical solvability of a problem on the motion of an isolated mass of a compressible liquid, St. Petersburg Math. J., 14 (2003), 53-74. |
[3] |
I. V. Denisova and V. A. Solonnikov, Classical solvability of a model problem in a half-space, related to the motion of an isolated mass of a compressible fluid, J. Math. Sci., 115 (2003), 2753-2765.
doi: 10.1023/A:1023365718404. |
[4] |
R. Denk, M. Hieber and J. Prüß, $\mathcalR$-boundedness, Fourier multiplier and problems of elliptic and parabolic type, Memories of AMS., 166 (2003), viii+114 pp.
doi: 10.1090/memo/0788. |
[5] |
Y. Enomoto, L. v. Below and Y. Shibata, On some free boundary problem for a compressible barotopic viscous fluid flow, Ann Univ Ferrara, 60 (2014), 55-89.
doi: 10.1007/s11565-013-0194-8. |
[6] |
Y. Enomoto and Y. Shibata, On the $\mathcalR$-sectoriality and its application to some mathematical study of the viscous compressible fluids, Funkcial. Ekvac., 56 (2013), 441-505.
doi: 10.1619/fesi.56.441. |
[7] |
D. Götz and Y. Shibata, On the $\mathcalR$-boundedness of the solution operators in the study of the compressible viscous fluid with free boundary condition, Asymptotic Analysis, 90 (2014), 207-236.
doi: 10.3233/ASY-141238. |
[8] |
T. Kubo, Y. Shibata and K. Soga, On the $\mathcalR$-boundedness for the Two phase prolem: Compressible-incompressible model prolem, Boundary Value Problems, 2014 (2014), 33p.
doi: 10.1186/s13661-014-0141-3. |
[9] |
P. Scchi and A. Valli, A free boundary problem for compressible viscous fluid, J. Reine Angew, Math., 341 (1983), 1-31.
doi: 10.1515/crll.1983.341.1. |
[10] |
Y. Shibata and S. Shimizu, On the $L_p$-$L_q$ maximal regularity of the Neumann problem for the Stokes equations in a bounded domain, J.Reine Angew. Math., 615 (2008), 157-209.
doi: 10.1515/CRELLE.2008.013. |
[11] |
Y. Shibata and K. Tanaka, On a resolvent problem for the linealized system from the dynamical system describing the compressible viscous fluid motion, Math. Mech. Appl. Sci., 27 (2004), 1579-1606.
doi: 10.1002/mma.518. |
[12] |
V. A. Solonnikov and A. Tani, Free boundary problem for a viscous compressible flow with the surface tension, Constantin Carathéodory: An International Tribute (Ih. M. Rassias, ed.), Vol. 1,2, World Sci. Publishing, Teaneck, (1991), 1270-1303. |
[13] |
G. Ströhmer, About the resolvent of an operator from fluid dynamics, Math. Z., 194 (1987), 183-191.
doi: 10.1007/BF01161967. |
[14] |
A. Tani, On the free boundary value problem for compressible viscous fluid motion, J. Math. Kyoto Univ., 21 (1981), 839-859. |
[15] |
A. Tani, Two-phase free boundary problem for compressible viscous fluid motion, J. Math. Kyoto Univ., 24 (1984), 243-267. |
[16] |
L. Weis, Operator-valued Fourier multiplier theorems and maximal $L_p$-regularity, Math. Ann., 319 (2001), 735-758.
doi: 10.1007/PL00004457. |
show all references
References:
[1] |
I. V. Denisova, Evolution of compressible and imcompressible fluids separated by a closed interface, Interface Free Bound., 2 (2000), 283-312.
doi: 10.4171/IFB/21. |
[2] |
I. V. Denisova and V. A. Solonnikov, Classical solvability of a problem on the motion of an isolated mass of a compressible liquid, St. Petersburg Math. J., 14 (2003), 53-74. |
[3] |
I. V. Denisova and V. A. Solonnikov, Classical solvability of a model problem in a half-space, related to the motion of an isolated mass of a compressible fluid, J. Math. Sci., 115 (2003), 2753-2765.
doi: 10.1023/A:1023365718404. |
[4] |
R. Denk, M. Hieber and J. Prüß, $\mathcalR$-boundedness, Fourier multiplier and problems of elliptic and parabolic type, Memories of AMS., 166 (2003), viii+114 pp.
doi: 10.1090/memo/0788. |
[5] |
Y. Enomoto, L. v. Below and Y. Shibata, On some free boundary problem for a compressible barotopic viscous fluid flow, Ann Univ Ferrara, 60 (2014), 55-89.
doi: 10.1007/s11565-013-0194-8. |
[6] |
Y. Enomoto and Y. Shibata, On the $\mathcalR$-sectoriality and its application to some mathematical study of the viscous compressible fluids, Funkcial. Ekvac., 56 (2013), 441-505.
doi: 10.1619/fesi.56.441. |
[7] |
D. Götz and Y. Shibata, On the $\mathcalR$-boundedness of the solution operators in the study of the compressible viscous fluid with free boundary condition, Asymptotic Analysis, 90 (2014), 207-236.
doi: 10.3233/ASY-141238. |
[8] |
T. Kubo, Y. Shibata and K. Soga, On the $\mathcalR$-boundedness for the Two phase prolem: Compressible-incompressible model prolem, Boundary Value Problems, 2014 (2014), 33p.
doi: 10.1186/s13661-014-0141-3. |
[9] |
P. Scchi and A. Valli, A free boundary problem for compressible viscous fluid, J. Reine Angew, Math., 341 (1983), 1-31.
doi: 10.1515/crll.1983.341.1. |
[10] |
Y. Shibata and S. Shimizu, On the $L_p$-$L_q$ maximal regularity of the Neumann problem for the Stokes equations in a bounded domain, J.Reine Angew. Math., 615 (2008), 157-209.
doi: 10.1515/CRELLE.2008.013. |
[11] |
Y. Shibata and K. Tanaka, On a resolvent problem for the linealized system from the dynamical system describing the compressible viscous fluid motion, Math. Mech. Appl. Sci., 27 (2004), 1579-1606.
doi: 10.1002/mma.518. |
[12] |
V. A. Solonnikov and A. Tani, Free boundary problem for a viscous compressible flow with the surface tension, Constantin Carathéodory: An International Tribute (Ih. M. Rassias, ed.), Vol. 1,2, World Sci. Publishing, Teaneck, (1991), 1270-1303. |
[13] |
G. Ströhmer, About the resolvent of an operator from fluid dynamics, Math. Z., 194 (1987), 183-191.
doi: 10.1007/BF01161967. |
[14] |
A. Tani, On the free boundary value problem for compressible viscous fluid motion, J. Math. Kyoto Univ., 21 (1981), 839-859. |
[15] |
A. Tani, Two-phase free boundary problem for compressible viscous fluid motion, J. Math. Kyoto Univ., 24 (1984), 243-267. |
[16] |
L. Weis, Operator-valued Fourier multiplier theorems and maximal $L_p$-regularity, Math. Ann., 319 (2001), 735-758.
doi: 10.1007/PL00004457. |
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