TY - JOUR
T1 - On the Existence for the Free Interface 2D Euler Equation with a Localized Vorticity Condition
AU - Kukavica, Igor
AU - Tuffaha, Amjad
AU - Vicol, Vlad
AU - Wang, Fei
N1 - Funding Information:
I.K. and F.W. were supported in part by the NSF Grant DMS-1311943, while V.V. was supported in part by the NSF Grant DMS-1514771 and an A.P. Sloan fellowship.
Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - We prove a local-in-time existence of solutions result for the two dimensional incompressible Euler equations with a moving boundary, with no surface tension, under the Rayleigh–Taylor stability condition. The main feature of the result is a local regularity assumption on the initial vorticity, namely H1.5 + δ Sobolev regularity in the vicinity of the moving interface in addition to the global regularity assumption on the initial fluid velocity in the H2 + δ space. We use a special change of variables and derive a priori estimates, establishing the local-in-time existence in H2 + δ. The assumptions on the initial data constitute the minimal set of assumptions for the existence of solutions to the rotational flow problem to be established in 2D.
AB - We prove a local-in-time existence of solutions result for the two dimensional incompressible Euler equations with a moving boundary, with no surface tension, under the Rayleigh–Taylor stability condition. The main feature of the result is a local regularity assumption on the initial vorticity, namely H1.5 + δ Sobolev regularity in the vicinity of the moving interface in addition to the global regularity assumption on the initial fluid velocity in the H2 + δ space. We use a special change of variables and derive a priori estimates, establishing the local-in-time existence in H2 + δ. The assumptions on the initial data constitute the minimal set of assumptions for the existence of solutions to the rotational flow problem to be established in 2D.
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U2 - 10.1007/s00245-016-9346-4
DO - 10.1007/s00245-016-9346-4
M3 - Article
AN - SCOPUS:84962682774
SN - 0095-4616
VL - 73
SP - 523
EP - 544
JO - Applied Mathematics and Optimization
JF - Applied Mathematics and Optimization
IS - 3
ER -