On the free boundary problem of three‐dimensional incompressible Euler equations

By Ping Zhang, Zhifei Zhang. 2008

191 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a25e2ab8aab76b97897c564ed4e602cd958d91d5

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Finite time singularities for the free boundary incompressible Euler equations (2011, unknown): “See Christodoulou-Lindblad [12], Lindblad [23], Coutand-Shkoller [16], Shatah-Zeng [28] and Zhang-Zhang [35].”
Well-Posedness in Smooth Function Spaces for the Moving-Boundary Three-Dimensional Compressible Euler Equations in Physical Vacuum (2012, background): “We refer the reader to [1,9,19,21,32,34,41,42,45], and [46] for a partial list of papers on this topic.”
On the Cauchy problem for gravity water waves (2012, methodology): “Several extensions of their results have been obtained by different methods (see [22, 31, 32, 33, 35, 41, 54, 55, 59] for recent results and the surveys [11, 29, 36] for more references).”
Well‐posedness of Compressible Euler Equations in a Physical Vacuum (2010, background): “For multi-dimensional flows, parallel to a lot of activity and important progress in free surface boundary problems, in particular regarding incompressible fluids [2, 3, 4, 11, 20, 35, 58, 61, 64], more recently, there are some works trying to prove the local well-posedness of physical vacuum in 3D.”
Local well-posedness of the viscous surface wave problem without surface tension (2013, methodology): “Local well-posedness without the irrotationality assumption was proved with a modified surface formulation by Zhang-Zhang [36] and with the original formulation by Christodoulou-Lindblad [10], Lindblad [23], Coutand-Shkoller”
Well‐posedness in smooth function spaces for moving‐boundary 1‐D compressible euler equations in physical vacuum (2009, background): “tions when arbitrary domains are considered, or complex analysis tools for the irrotational problem with inﬁnite depth. We refer the reader to [2], [10], [20], [22], [33], [35], [41], [42], [43], and [46] for a partial list of papers on this topic. 6 D. COUTAND AND S. SHKOLLER 1.8.2. The compressibl”
Almost Exponential Decay of Periodic Viscous Surface Waves without Surface Tension (2013, unknown): “Ē−2N (0) + ∫ t 0 Eθ2ND2N + εD2N + ε−8N−1D̄02N .”
Decay of viscous surface waves without surface tension (2010, unknown): “22”
Two dimensional water waves in holomorphic coordinates II: global solutions (2014, unknown): “Without being exhaustive, we list some of the more recent references [2, 1, 5, 6, 7, 12, 4, 13, 15, 16, 18, 20, 22].”
Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations (2012, methodology): “Note that by using the equation for the vorticity, one can easily propagate higher normal regularity and thus recover the results of [34, 49, 61].”