6 papers
Full-Density Degenerate Stagnation Points for Water Waves with General Vorticity
Lili Du, Chunlei Yang
In this paper, we revisit the singular asymptotics of the free surface near stagnation points for two-dimensional traveling gravity water waves with vorticity. We prove the nonexis…
Geometric structure of singular free boundary points for the logarithmic obstacle problem
Lili Du, Xu Tang, Yi Zhou
In the previous work [Interfaces Free Bound., 19, 351--369, 2017], de Queiroz and Shahgholian established the optimal regularity of solutions for the ob…
Singular profile of free boundary of incompressible inviscid fluid with external force
Lili Du, Yang Pu, Jing Yang
This article is devoted to investigate the singular profile of the free boundary of two-dimensional incompressible inviscid fluid with external force near the stagnation point. Mor…
Helically symmetric solution of 3D Euler equations with vorticity and its free boundary
Lili Du, Feng Ji
This paper investigates an incompressible steady free boundary problem of Euler equations with helical symmetry in dimensions and with nontrivial vorticity. The velocity field…
Proof of the Stokes conjecture for compressible gravity water waves
Lili Du, Chunlei Yang
In 1880, Stokes examined an incompressible irrotational periodic traveling water wave under the influence of gravity and conjectured the existence of an extreme wave with a corner…
Singular and regular analysis for the free boundaries of two-phase inviscid fluids in gravity field
Lili Du, Feng Ji
In this paper, we consider a free boundary problem of two-phase inviscid incompressible fluid in gravity field. The presence of the gravity field induces novel phenomena that there…