Аннотация:
Доказана локальная по времени разрешимость задачи со свободной границей,
описывающей эволюцию конечной массы вязкой несжимаемой жидкости в Rn, n=2,3, без учета поверхностного натяжения. Даны достаточные условия продолжимости решения на бесконечный интервал времени t>0. Решение получено в пространстве W2,1p с p>n.
Библиография: 19 названий.
Образец цитирования:
В. А. Солонников, “О неустановившемся движении изолированного объема вязкой несжимаемой жидкости”, Изв. АН СССР. Сер. матем., 51:5 (1987), 1065–1087; Math. USSR-Izv., 31:2 (1988), 381–405
Takayoshi Ogawa, Senjo Shimizu, “Free boundary problems of the incompressible Navier–Stokes equations with non-flat initial surface in the critical Besov space”, Math. Ann., 2024
Takayoshi OGAWA, Senjo SHIMIZU, “Maximal L1-regularity and free boundary problems for the incompressible Navier–Stokes equations in critical spaces”, J. Math. Soc. Japan, 76:2 (2024)
C. Denis, A. F. M. ter Elst, “The Stokes Dirichlet-to-Neumann operator”, J. Evol. Equ., 24:2 (2024)
Youyi Zhao, “On the inhibition of Rayleigh–Taylor instability by surface tension in stratified incompressible viscous fluids under Lagrangian coordinates”, DCDS, 2024
Takayoshi Ogawa, the author, “Critical structures and regularity for nonlinear evolutional partial differential equations”, Sugaku Expositions, 37:1 (2024), 23
I. V. Denisova, V. A. Solonnikov, “Stability of the Rotation of a Two-Component Drop with Self-Gravity”, J Math Sci, 283:5 (2024), 756
Vladimir Kozlov, Jürgen Rossmann, “On the Neumann problem for the nonstationary Stokes system in angles and cones”, Mathematische Nachrichten, 296:4 (2023), 1504
Hantaek Bae, Woojae Lee, Jaeyong Shin, “Global existence and decay rates of solutions to the viscous water-waves system”, Nonlinear Analysis, 224 (2022), 113062
Kenta Oishi, Yoshihiro Shibata, “On the Global Well-Posedness and Decay of a Free Boundary Problem of the Navier–Stokes Equation in Unbounded Domains”, Mathematics, 10:5 (2022), 774
I. V. Denisova, V. A. Solonnikov, “Stability of the rotation of a two-phase drop with self-gravity”, Краевые задачи математической физики и смежные вопросы теории функций. 49, К юбилею Григория Александровича СЕРЕГИНА, Зап. научн. сем. ПОМИ, 508, ПОМИ, СПб., 2021, 89–123
Takayoshi Ogawa, Senjo Shimizu, “Maximal L1-regularity of the heat equation and application to a free boundary problem of the Navier-Stokes equations near the half-space”, J Elliptic Parabol Equ, 7:2 (2021), 509
I. V. Denisova, V. A. Solonnikov, Advances in Mathematical Fluid Mechanics, Motion of a Drop in an Incompressible Fluid, 2021, 1
I. V. Denisova, V. A. Solonnikov, Advances in Mathematical Fluid Mechanics, Motion of a Drop in an Incompressible Fluid, 2021, 233
Yongting Huang, Tao Luo, “Compressible viscous heat-conducting surface wave without surface tension”, Journal of Mathematical Physics, 62:6 (2021), 061501
I. V. Denisova, V. A. Solonnikov, Advances in Mathematical Fluid Mechanics, Motion of a Drop in an Incompressible Fluid, 2021, 139
Takayoshi Ogawa, Senjo Shimizu, “Global well-posedness for the incompressible Navier–Stokes equations in the critical Besov space under the Lagrangian coordinates”, Journal of Differential Equations, 274 (2021), 613
Irina Vladimirovna Denisova, Vsevolod Alexeevich Solonnikov, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, 1
Helmut Abels, Harald Garcke, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, 1267
Irina Vladimirovna Denisova, Vsevolod Alexeevich Solonnikov, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, 1947
Vsevolod Alexeevich Solonnikov, Irina Vladimirovna Denisova, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, 1135
Цитирование в формате AMSBIB
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