On the 90th birthday of Vsevolod Alekseevich Solonnikov

G. I. Bizhanova   ; I. V. Denisova   ; A. I. Nazarov   ; K. I. Pileckas   ; V. V. Pukhnachev   ; S. I. Repin   ; J.-F. Rodrigues   ; G. A. Seregin   ; N. N. Uraltseva   ; E. V. Frolova

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 78 (2023) no. 5, pp. 971-981

Bibliographie

[1] V. A. Solonnikov, “Linear differential equations with a small parameter in the highest derivative term”, Dokl. Akad. Nauk SSSR, 119:3 (1958), 454–457 (Russian) | MR | Zbl

[2] V. A. Solonnikov, “A priori estimates for certain boundary value problems”, Soviet Math. Dokl., 2 (1961), 723–727 | MR | Zbl

[3] V. A. Solonnikov, “A priori estimates for second-order parabolic equations”, Amer. Math. Soc. Transl. Ser. 2, 65, Amer. Math. Soc., Providence, RI, 1967, 51–137 | DOI | MR | Zbl

[4] V. Solonnikov, “On estimates of Green's tensors for certain boundary problems”, Soviet Math. Dokl., 1 (1960), 128–131 | MR | Zbl

[5] V. A. Solonnikov, “On general boundary problems for systems which are elliptic in the sense of A. Douglis and L. Nirenberg. I”, Amer. Math. Soc. Transl. Ser. 2, 56, Amer. Math. Soc., Providence, RI, 1964, 193–232 | DOI | MR | Zbl

[6] V. A. Solonnikov, “General boundary value problems for Douglis–Nirenberg elliptic systems. II”, Proc. Steklov Inst. Math., 92 (1968), 269–339 | MR | Zbl

[7] V. A. Solonnikov, “On boundary value problems for linear parabolic systems of differential equations of general form”, Proc. Steklov Inst. Math., 83 (1965), 1–184 | MR | Zbl

[8] O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural'ceva (Uraltseva), Linear and quasi-linear equations of parabolic type, Transl. Math. Monogr., 23, Amer. Math. Soc., Providence, RI, 1968, xi+648 pp. | DOI | MR | Zbl

[9] V. Zaionchkovskii (Zaja̧czkowski) and V. A. Solonnikov, “Neumann problem for second-order elliptic equations in domains with edges on the boundary”, J. Soviet Math., 27 (1984), 2561–2586 | DOI | MR | Zbl

[10] V. A. Solonnikov, “Solvability of the classical initial-boundary-value problems for the heat-conduction equation in a dihedral angle”, J. Soviet Math., 32 (1986), 526–546 | DOI | MR | Zbl

[11] V. A. Solonnikov and E. V. Frolova, “On a problem with the third boundary condition for the Laplace equation in a plane angle, and its applications to parabolic problems”, Leningrad Math. J., 2:4 (1991), 891–916 | MR | Zbl

[12] V. P. Il'in and V. A. Solonnikov, “On some properties of differentiable functions of several variables”, Amer. Math. Soc. Transl. Ser. 2, 81, Amer. Math. Soc., Providence, RI, 1969, 67–90 | DOI | MR | Zbl

[13] K. K. Golovkin and V. A. Solonnikov, “Estimates for integral operators in translation-invariant norms”, Amer. Math. Soc. Transl. Ser. 2, 61, Amer. Math. Soc., Providence, RI, 1967, 97–112 ; II, Proc. Steklov Inst. Math., 92 (1968), 3–32 | DOI | MR | Zbl | MR | Zbl

[14] K. K. Golovkin and V. A. Solonnikov, “Estimates of convolution operators”, Semin. Math., 7, V. A. Steklov Math. Inst., Leningrad, 1968, 1–36 | MR | Zbl

[15] K. K. Golovkin and V. A. Solonnikov, “On the first boundary problem for the nonstationary Navier–Stokes equations”, Soviet Math. Dokl., 2 (1961), 1188–1193 | MR | Zbl

[16] V. A. Solonnikov, “Estimates of the solutions of a nonstationary linearized system of Navier–Stokes equations”, Amer. Math. Soc. Transl. Ser. 2, 75, Amer. Math. Soc., Providence, RI, 1968, 1–116 | DOI | MR | Zbl

[17] V. A. Solonnikov, “On the differentiability properties of the solution of the first boundary-value problem for a non-stationary system of Navier–Stokes equations”, Boundary-value problems of mathematical physics. 2, Tr. Mat. Inst. Steklov., 73, Nauka, Moscow–Leningrad, 1964, 221–291 (Russian) | MR | Zbl

[18] V. A. Solonnikov and V. E. Shchadilov, “A certain boundary value problem for the stationary system of Navier–Stokes equations”, Proc. Steklov Inst. Math., 125 (1973), 186–199 | MR | Zbl

[19] O. A. Ladyzhenskaya and V. A. Solonnikov, “Some problems of vector analysis and generalized formulations of boundary-value problems for the Navier–Stokes equations”, J. Soviet Math., 10:2 (1978), 257–286 | DOI | MR | Zbl

[20] O. A. Ladyzhenskaya and V. A. Solonnikov, “On the solvability of boundary and initial-boundary value problems for Navier–Stokes equations in domains with non-compact boundaries”, Vestn. Lenongr. Univ., 13:3 (1977), 39–47 (Russian) | MR | Zbl

[21] O. A. Ladyzhenskaya and V. A. Solonnikov, “Determination of the solutions of boundary value problems for stationary Stokes and Navier–Stokes equations having an unbounded Dirichlet integral”, J. Soviet Math., 21:5 (1983), 728–761 | DOI | MR | Zbl

[22] V. A. Solonnikov and K. I. Piletskas (Pileckas), “Certain spaces of solenoidal vectors and the solvability of the boundary problem for the Navier–Stokes system of equations in domains with noncompact boundaries”, J. Soviet Math., 34:6 (1986), 2101–2111 | DOI | MR | Zbl

[23] V. A. Solonnikov, “On problems of the hydrodynamics of a viscous incompressible fluid in domains with noncompact boundaries”, St. Petersburg Math. J., 4:6 (1993), 1081–1102 | MR | Zbl

[24] O. A. Ladyzhenskaya and V. A. Solonnikov, “Solution of some non-stationary problems of magnetohydrodynamics for a viscous incompressible fluid”, Mathematica problems in hydrodynamics and magnetohydrodynamics for a viscous incompressible fluid, Tr. Mat. Inst. Steklov., 59, Publishing house of the USSR Academy of Sciences, Moscow–Leningrad, 1960, 115–173 (Russian) | MR

[25] V. A. Solonnikov, “Some stationary boundary-value problems in magnetohydrodynamics”, Mathematica problems in hydrodynamics and magnetohydrodynamics for a viscous incompressible fluid, Tr. Mat. Inst. Steklov., 59, Publishing house of the USSR Academy of Sciences, Moscow–Leningrad, 1960, 174–187 (Russian) | MR

[26] O. A. Ladyzhenskaya and V. A. Solonnikov, “The linearization principle and invariant manifolds for problems of magnetohydrodynamics”, J. Soviet Math., 8 (1977), 384–422 | DOI | MR | Zbl

[27] V. A. Solonnikov and E. V. Frolova, “Solvability of a free boundary problem of magnetohydrodynamics in an infinite time interval”, J. Math. Sci. (N. Y.), 195:1 (2013), 76–97 | DOI | MR

[28] V. A. Solonnikov, “$L_p$-theory of free boundary problems of magnetohydrodynamics in multi-connected domains”, Ann. Univ. Ferrara Sez. VII Sci. Mat., 60:1 (2014), 263–288 | DOI | MR | Zbl

[29] V. A. Solonnikov, “Solvability of a problem on the plane motion of a heavy viscous incompressible capillary liquid partially filling a container”, Math. USSR-Izv., 14:1 (1980), 193–221 | DOI | MR | Zbl

[30] V. A. Solonnikov, “Solvability of three-dimentional problem with a free boundary for a stationary system of Navier–Stokes equations”, J. Soviet Math., 21:3 (1983), 427–450 | DOI | MR | Zbl

[31] G. I. Bizhanova and V. A. Solonnikov, “Free boundary problems for second order parabolic equations”, St. Petersburg Math. J., 12:6 (2001), 949–981 | MR | Zbl

[32] V. A. Solonnikov and E. V. Frolova, “$L_p$-theory for the Stefan problem”, J. Math. Sci. (N. Y.), 99:1 (2000), 989–1006 | DOI | MR | Zbl

[33] V. A. Solonnikov and E. V. Frolova, “Justification of a quasistationary approximation for the Stefan problem”, J. Math. Sci. (N. Y.), 152:5 (2008), 741–768 | DOI | MR

[34] V. A. Solonnikov, “Solvability of a problem on the motion of a viscous incompressible fluid bounded by a free surface”, Math. USSR-Izv., 11:6 (1977), 1323–1358 | DOI | MR | Zbl

[35] V. A. Solonnikov, “Unsteady motion of a finite mass of fluid, bounded by a free surface”, J. Soviet Math., 40:5 (1988), 672–686 | DOI | MR | Zbl

[36] I. S. Mogilevskii and V. A. Solonnikov, “Solvability of a noncoercive initial-boundary value problem for a Stokes system in Holder classes of functions (half-space case)”, Z. Anal. Anwendungen, 8:4 (1989), 329–347 (Russian) | DOI | MR | Zbl

[37] I. S. Mogilevskii and V. A. Solonnikov, “On the solvability of an evolution free boundary problem for the Navier–Stokes equations in Hölder spaces of functions”, Mathematical problems relating to Navier–Stokes equations, Ser. Adv. Math. Appl. Sci., 11, World Sci. Publ., River Edge, NJ, 1992, 105–181 | DOI | MR | Zbl

[38] V. A. Solonnikov, “Estimates of solutions of the second initial boundary-value problem for the Stokes system in the spaces of functions having Hölder continuous derivatives with respect to spatial variables”, J. Math. Sci. (N. Y.), 109:5 (2002), 1997–2017 | DOI | MR | Zbl

[39] 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. (N. Y.), 115:6 (2003), 2753–2765 | DOI | MR | Zbl

[40] I. V. Denisova and V. A. Solonnikov, “Classical solvability of a problem on the motion of an isolated mass of compressible fluid”, St. Petersburg Math. J., 14:1 (2002), 53–74 | MR | Zbl

[41] V. A. Solonnikov and A. Tani, “Free boundary problem for a viscous compressible flow with a surface tension”, Constantin Carathéodory: an international tribute, World Sci. Publ., Teaneck, NJ, 1991, 1270–1303 | DOI | MR | Zbl

[42] I. V. Denisova and V. A. Solonnikov, “$L_2$-theory for two incompressible fluids separated by a free interface”, Topol. Methods Nonlinear Anal., 52:1 (2018), 213–238 | DOI | MR | Zbl

[43] M. Padula and V. A. Solonnikov, “On the global existence of nonsteady motions of a fluid drop and their exponential decay to a uniform rigid rotation”, Topics in mathematical fluid mechanics, Quad. Mat., 10, Dept. Math., Seconda Univ. Napoli, Caserta, 2002, 185–218 | MR | Zbl

[44] V. A. Solonnikov, “Estimate of the generalized energy in a free-boundary problem for a viscous incompressible fluid”, J. Math. Sci. (N. Y.), 120:5 (2004), 1766–1783 | DOI | MR | Zbl

[45] V. A. Solonnikov, “Lectures on evolution free boundary problems: classical solutions”, Mathematical aspects of evolving interfaces (Funchal 2000), Lecture Notes in Math., 1812, Springer-Verlag, Berlin, 2003, 123–175 | DOI | MR | Zbl

[46] V. A. Solonnikov, “On the stability of axially symmetric equilibrium figures of a rotating viscous incompressible fluid”, St. Petersburg Math. J., 16:2 (2005), 377–400 | DOI | MR | Zbl

[47] V. Solonnikov, “On problem of stability of equilibrium figures of uniformly rotating viscous incompressible liquid”, Instability in models connected with fluid flows. II, Int. Math. Ser. (N. Y.), 7, Springer, New York, 2008, 189–254 | DOI | MR | Zbl

[48] V. A. Solonnikov and I. V. Denisova, “Classical well-posedness of free boundary problems in viscous incompressible fluid mechanics”, Handbook of mathematical analysis in mechanics of viscous fluids, Springer, Cham, 2018, 1135–1220 | DOI | MR

[49] I. V. Denisova and V. A. Solonnikov, “Local and global solvability of free boundary problems for the compressible Navier–Stokes equations near equilibria”, Handbook of mathematical analysis in mechanics of viscous fluids, Springer, Cham, 2018, 1947–2035 | DOI | MR

[50] I. V. Denisova and V. A. Solonnikov, Motion of a drop in an incompressible fluid, Adv. Math. Fluid Mech., Lect. Notes Math. Fluid Mech., Birkhäuser/Springer, Cham, 2021, vii+316 pp. | DOI | MR | Zbl

[51] V. A. Solonnikov, “On the problem of non-stationary motion of two viscous incompressible liquids”, J. Math. Sci. (N. Y.), 142:1 (2007), 1844–1866 | DOI | MR | Zbl

[52] I. V. Denisova and V. A. Solonnikov, “Rotation problem for a two-phase drop”, J. Math. Fluid Mech., 24 (2022), 40, 26 pp. | DOI | MR | Zbl

[53] V. A. Solonnikov, “$L_2$-theory for two viscous fluids of different types: compressible and incompressible”, St. Petersburg Math. J., 32:1 (2021), 91–137 | DOI | MR | Zbl

[54] V. A. Solonnikov and N. N. Uraltseva, “Sobolev spaces”, Publishing house of Lenngrad State University, Leningrad, 1981, 129–199 (Russian)

[55] K. Pileckas and V. A. Solonnikov, “Viscous incompressible free-surface flow down an inclined perturbed plane”, Ann. Univ. Ferrara Sez. VII Sci. Mat., 60:1 (2014), 225–244 | DOI | MR | Zbl