Geodesic
Estimates of a single problem of electrodynamics arising in magnetic hydrodynamics in space $W_{p}^{2,1} (Q_{T} ), p>1$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1787-1796.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, unique solvability is obtained and estimates of solutions to the problem of magnetic hydrodynamics are obtained.
Keywords: boundary value problem, magnetic hydrodynamics, Hölder conditions, Volterra–Fredholm type, heat equation. 
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Sh. Sakhaev. Estimates of a single problem of electrodynamics arising in magnetic hydrodynamics in space $W_{p}^{2,1} (Q_{T} ), p>1$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1787-1796. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a102/

[1] O.A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, Science Publishers, New York etc, 1969 | MR | Zbl

[2] Sh. Sakhaev, “Resheniye pervoy nachal'no-krayevoy zadachi dlya nestatsionarnoy sistemy uravneniy Maksvella”, Trudy Inst. Matem. Mekh. Akad. Nauk KazSSR, 1972:2 (1972), 69–77

[3] Sh. Sakhaev, V.A. Solonnikov, “Estimations of the solutions of a certain boundary value problem in magnetohydrodynamics”, Proc. Steklov Inst. Math., 127 (1975), 87–108 | MR | Zbl

[4] V.A. Solonnikov, “A study of overdetermined elliptic boundary value problems in K.K. Golovkin's fractional spaces”, Proc. Steklov Inst. Math., 127 (1975), 109–134 | MR | Zbl

[5] L.N. Slobodetskij, “Generalized Sobolev spaces and their application to boundary problems for partial differential equations”, Am. Math. Soc., Transl., II. Ser., 57 (1966), 207–275 | DOI | Zbl

[6] V.A. Solonnikov, “A priori estimates for solutions of second-order equations of parabolic type”, Tr. Mat. Inst. Steklova, 70, 1964, 133–212 | MR | Zbl

[7] A.P. Calderon, A. Zygmund, “On the existence of certain singular integrals”, Acta Math., 88 (1952), 85–139 | DOI | MR | Zbl

[8] S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, v. I, Inostrannaya literatura, M., 1962 | MR | Zbl

[9] Sh. Sahaev, V.A. Solonnikov, “On the proof of the solvability of a linear problem arising in magnetohydrodynamics with the method of integral equations”, St. Petersburg Math. J., 26:6 (2015), 985–1003 | DOI | MR | Zbl

[10] Sh. Sahaev, V.A. Solonnikov, “On some stationary problems of magnetohydrodynamics in multi-connected domains”, J. Math. Sci., New York, 185:5 (2012), 728–741 | DOI | MR | Zbl

[11] Sh. Sakhaev, “On one analog of Green's formula and its applications in electrodynamics”, J. Math. Sci., New York, 117:2 (2003), 4008–4019 | DOI | MR | Zbl

[12] Sh. Sakhaev, “The boundary-value problems for a system similar to the Maxwell system”, J. Math. Sci., New York, 111:5 (2002), 3806–3811 | DOI | MR | Zbl

[13] N.M. Gunter, Theory of the potential and its application to the basic problems of mathematical physics, Gostekhizdat, M., 1953 | MR | Zbl

[14] H. Weyl, “The method of orthogonal projection in potential theory”, Duke Math. J., 7 (1940), 411–444 | DOI | MR | Zbl

[15] V.A. Solonnikov, “Otsenki resheniy nestatsionarnoy sistemy Nav'ye-Stoksa”, Zap. nauchn. sem. LOMI, 38, 1973, 153–231 | Zbl

[16] V.A. Solonnikov, On boundary value problems for linear parabolic systems of differential equations of general form, Proc. Steklov Inst. Math., 83, 1965 | MR | Zbl