5 papers · 1 filter
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…
The singularity at degenerate points in steady axisymmetric compressible free surface flows with gravity
Lili Du, Chunlei Yang
In this paper, we analyze the singular shape of the free boundary at degenerate points in a three dimensional axisymmetric compressible gravity flow. For all possible degenerate po…
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…
The free boundary of steady axisymmetric inviscid flow with vorticity II: near the non-degenerate points
Lili Du, Chunlei Yang
This is the sequel of the recent work (Du, Huang, Pu, Commun. Math. Phys, 2023, doi: 10.1007/s00220-023-04651-7) on axially symmetric gravity water waves with general vorticities,…
The free boundary for a semilinear non-homogeneous Bernoulli problem
Lili Du, Chunlei Yang
In the classical homogeneous one-phase Bernoulli-type problem, the free boundary consists of a "regular" part and a "singular" part, as Alt and Caffarelli have shown in their pione…