Speaker: Prof. Denisova Irina Vlad.，Institute for Problems in Mechanical Engineering , Russian Academy of Sciences
Inviter: 郝成春

Title: Global solvability of a problem governing the motion of a drop in an incompressible capillary fluid

Language: English

Time & Venue: 2026.05.22 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.