### On the Faedo-Galerkin method for a free boundary problem for incompressible viscous magnetohydrodynamics

DOI: http://dx.doi.org/10.12775/TMNA.2018.011

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#### References

E.B. Bykhovsky, Solvability of mixed problem for the Maxwell equations for ideal conductive boundary, Vestn. Len. Univ. Ser. Mat. Mekh. Astr. 13 (1957), 50–66. (in Russian)

G.H.A. Cole, Fluid Dynamics, London & Colchester, 1962.

E. Frolova, Free boundary problem of magnetohydrodynamics, Zap. Nauchn. Sem. POMI 425 (2014), 149–178.

E. Frolova and V.A. Solonnikov, Solvability of a free boundary problem of magnetohydrodynamics in an infinite time interval, Zap. Nauchn. Sem. POMI 410 (2013), 131–167.

P. Kacprzyk, Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid, Appl. Math. 30 (2003), 461–488.

P. Kacprzyk, Almost global solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid, Appl. Math. 31 (2004), 69–77.

P. Kacprzyk, Free boundary problem for the equations of magnetohydrodynamic incompressible viscous fluid, Appl. Math. 34 (2007), 75–95.

P. Kacprzyk, Local free boundary problem for incompressible magnetohydrodynamics, Dissertationes Math. 509 (2015), 1–52.

P. Kacprzyk, Global free boundary problem for incompressible magnetohydrodynamics, Dissertationes Math. 510 (2015), 1–44.

L. Kapitański and K. Pileckas, On some problems of vector analysis, Zap. Nauchn. Sem. LOMI 138 (1984), 65–85. (in Russian)

N.E. Kochin, Vectorial Calculus and Introduction to Tensor Calculus, Moscow, 1951. (in Russian)

O.A. Ladyzhenskaya, Boundary Value Problems for Mathematical Physics, Moscow, 1973. (in Russian)

O.A. Ladyzhenskaya, Krajewyje Zadaci Matematicieskoj Fizyki, Nauka, Moskwa, 1973. (in Russian)

O.A. Ladyzhenskaya and V.A. Solonnikov, Solvability of some nonstationary problems of magnetohydrodynamics for viscous incompressible fluids, Trudy Mat. Inst. Steklov 59 (1960), 115–173. (in Russian)

L.D. Landau, E.M. Lifshitz and L.P. Pitaevskiı̆, Electrodynamics of Continuous Media, second edition, Landau and Lifshitz Course of Theoretical Physics, Vol. 8.

M. Padula and V.A. Solonnikov, On free boundary problem of mhd, Zap. Nauchn. Sem. POMI 385 (2010); Kraevye Zadachi Matematicheskoj Fiziki i Smezhnye Voprosy Teorii Funktsii 41 (2010), 135–186; English transl.: J. Math. Sci. (N.Y.) 178 (2011), 313–344.

M. Sahaev and V.A. Solonnikov, On some stationary problems of magnetohydrodynamics in general domains, Zap. Nauchn. Sem. POMI 397 (2011), 126–149.

Y. Shibata and W.M. Zajączkowski, On local motion to a free boundary problem for incompressible viscous magnetohydrodynamics in the Lp -approach, Part 1.

Y. Shibata and W.M. Zajączkowski, On local motion to a free boundary problem for incompressible viscous magnetohydrodynamics in the Lp -approach, Part 2.

V.A. Solonnikov, Estimates of solutions to nonstationary linearized Navier–Stokes system, Trudy MIAN 70 (1964), 213–317. (in Russian)

V.A. Solonnikov, Estimates of solutions of an initial-boundary value problem for the linear non-stationary Navier–Stokes system, Zap. Nauchn. Sem. LOMI 59 (1976), 178–254. (in Russian)

V.A. Solonnikov, On an unsteady motion of an isolated volume of a visous incompressible fluid, Izv. Ross. Akad. Nauk Ser. Mat. 51 (1987), 1065–1087. (in Russian)

R. Temam, Navier–Stokes Equations: Theory and Numerical Analysis, American Mathematical Society, 2001.

W.M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Math. 324 (1993), pp. 101.

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