中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
偏微分方程研讨班
Speaker: Prof. Denisova Irina Vlad.
（Institute for Problems in Mechanical Engineering , Russian Academy of Sciences）
Inviter: 郝成春
Language: English
Title: Steady and unsteady free boundary problems in mathematical hydrodynamics.
Time & Venue: 2026年5月20日（星期三）14：00-16：00 & 南楼N913
Abstract: We consider mainly evolutionary free boundary problems. First, the problem concerning the evolution of an isolated mass of incompressible liquid is observed in the both cases: with surface tension on the free boundary and without it.Results concerning local and global-in-time classical solvability of such problems are given under certain assumptions on the data. Next, we discuss the analysis of a rotating fluid, including the stability problem. We state the problem governing the motion of a bubble in vacuum. The motion of two compressible fluids and fluids of different types, compressible and incompressible, separated by an unknown interface is also discussed.
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Title: Global solvability of a problem governing the motion of a drop in an incompressible capillary fluid.
Time & Venue: 2026年5月22日（星期五）14：00-16：00 & 南楼N913
Abstract: We deal with the motion of two immiscible incompressible fluids in a container. The liquids are separated by a closed unknown interface on which surface tension is taken into account. We study this problem in the H¨older spaces of functions. We prove that this problem is uniquely solvable in an infinite time interval provided that the initial velocity of the liquids and mass forces are small, while the initial configuration of the inner fluid is close to a ball with the center at the original. Moreover, we show that the velocity decays exponentially at infinity with respect to time and that the interface between the fluids tends to a sphere of the same radius as at initial moment, the center being different from the original in the general case. The proof is based on an exponential estimate of a generalized energy and on a local existence theorem for the problem.
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Title: Global existence theorem for the problem on two-phase capillary fluid motion in Oberbeck–Boussinesq approximation
Time & Venue: 2026年5月25日（星期一）14：00-16：00 & 南楼N913
Abstract:
References：
[1] Denisova I. V., Nechasova S., Oberbeck_x0016_Boussinesq approximation for the motion of two incompressible fluids, Zapiski nauchn. semin. POMI 362 (2008), 92-119 (English transl. in J. Math. Sci. 159, no. 4 (2009), 436-451).
[2] Padula M., On the exponential stability of the rest state of a viscous compressible fluid, J. Math. Fluid Mech. 1 (1999), 62–77.
[3] Denisova I. V., Solonnikov V. A., Global solvability of a problem governing the motion of two incompressible fluids in a container, Zapiski nauchn. semin. POMI 397 (2011), 20–52 (English transl. in J. Math. Sci. 185, no. 5 (2012), 668–686).
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Title:Stability of equilibrium figures of a rotating capillary two-layer incompressible fluid
Time & Venue: 2026年5月27日（星期三）14：00-16：00 & 南楼N913
Abstract:A uniformly rotating finite mass consisting of two immiscible viscous fluids is studied. This motion is described by a problem with unknown boundaries for the Navier-Stokes system. The interface between the fluids is assumed to be closed. Surface tension acts on both the interface and the outer free surface. The stability of a rotating two-layer drop with self-gravity is proved for sufficiently small initial data, angular velocity, and exponentially decreasing mass forces, as well as for the positivity of the second variation of the energy functional. The proof is based on an analysis of small perturbations of the equilibrium state of a rotating two-layer fluid.Furthermore, the existence of equilibrium figures is proven in the two-layer case when one (or both) of the fluids is compressible. If the pressure function is defined by a smooth, increasing density function for a compressible fluid, and the problem data satisfy a certain condition, then for a two-phase (two-layer compressible) fluid with low angular momentum, axisymmetric equilibrium figures similar to nested spheres exist.
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Title: On the stability of rotation of a two-phase fluid with a free boundary
Time & Venue: 2026年5月29日（星期五）14：00-16：00 & 南楼N913
Abstract:
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