ReferencesV. A. Solonnikov“$L_p$-estimates of solution of the free boundary problem for viscous compressible and incompressible fluids in the linear approximation”, Algebra i Analiz, 2020, Volume 32, Issue 3,Pages 254

$L_p$-estimates of solution of the free boundary problem for viscous compressible and incompressible fluids in the linear approximation
V. A. Solonnikov



References

1.	Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975
2.	Solonnikov V. A., “Apriornye otsenki dlya uravnenii vtorogo poryadka parabolicheskogo tipa”, Tr. Mat. in-ta AN SSSR, 70, 1964, 133–212
3.	Solonnikov V. A., “Ob odnoi nachalno-kraevoi zadache dlya uravnenii Stoksa, voznikayuschei pri izuchenii zadachi so svobodnoi granitsei”, Tr. Mat. in-ta RAN, 188, 1990, 150–188
4.	Lizorkin P. I., “K teorii multiplikatorov Fure”, Tr. Mat. in-ta RAN, 173, 1986, 149–163
5.	Denisova I. V., “Evolution of compressible and incompressible fluids separated by a closed interface”, Interfaces Free Bound., 2:3 (2000), 283–312
6.	Solonnikov V. A., “On the model problem arising in the study of motion of viscous compressible and incompressible fluids with a free interface”, Algebra i analiz, 30:3 (2018), 274–317
7.	Solonnikov V. A., “$L_p$-theory for the linear problem arising in the study of the motion of an isolated liquid mass”, J. Math. Sci. (N.Y.), 189:4 (2013), 699–733
8.	Volevich L. R., “Pazreshimost kraevykh zadach dlya obschikh ellipticheskikh sistem”, Mat. sb., 68:3 (1965), 373–416
9.	Mogilevskii I. Sh., “Otsenki resheniya obschei nachalno-kraevoi zadachi dlya lineinoi nestatsionarnoi sistemy uravnenii Nave–Stoksa v poluprostranstve”, Zap. nauch. semin. LOMI, 84, 1979, 147–173
10.	Denisova I. V., “On the energy inequality for the problem on the evolution of two fluids of different types without surface tension”, J. Math. Fluid Mech., 17:11 (2015), 163–198
11.	Kubo T., Shibata Y., Soga K., “$R$-boundedness for the two phase flow: compressible-incompressible model problem”, Bound. Value Probl., 141 (2014), 1–33
12.	Kubo T., Shibata Y., On the evolution of compressible and incompressible fluids with a sharp interface, Preprint, 2013
13.	Solonnikov V.A., “$L_2$-theory for two viscous fluids of different type: compressible and incompressible”, Algebra i analiz, 32:1 (2020), 121–186
14.	Denisova I. V., Solonnikov V. A., “Globalnaya razreshimost zadachi o dvizhenii dvukh neszhimaemykh kapillyarnykh zhidkostei v konteinere”, Zap. nauch. semin. LOMI, 397, 2011, 20–52
15.	Prüss J., Simonett G., Moving interfaces and quasilinear parabolic evolution equations, Monogr. Math., 105, Birkhäuser, Cham, 2016