On the Absence of ”splash” Singularities in the Case of Two-fluid Interfaces
نویسندگان
چکیده
We show that ”splash” singularities cannot develop in the case of locally smooth solutions of the two-fluid interfaces in two dimensions. More precisely, we show that the scenario of formation of singularities discovered by Castro–Córdoba–Fefferman–Gancedo–Gómez-Serrano [6] in the case of the water waves system, in which the interface remains locally smooth but self-intersects in finite time, is completely prevented in the case of two-fluid interfaces with positive densities.
منابع مشابه
No-splash theorems for fluid interfaces.
The article (1) by Gancedo and Strain in PNAS studies how singularities may develop in the initially smooth interfaces separating two or more incompressible fluids. The fluids and interfaces are assumed to evolve by either of the two standard systems of equations from fluid mechanics, namely the surface quasi-geostrophic (SQG) sharp front equation (2) or the Muskat equation (3). Gancedo and Str...
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