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Clifford Algebras and Dirac Operators in Harmonic Analysis
TLDR
In this article, Dirac operators and the spin group are used in the analysis of Euclidean spaces, where Dirac operator analysis is based on Clifford algebras.Abstract:
1. Clifford algebras 2. Dirac operators and Clifford analyticity 3. Dirac operators and the spin group 4. Dirac operators in the analysis on Euclidean space 5. Dirac operators in representation theory 6. Dirac operators in analysis.read more
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Well-posedness in Sobolev spaces of the full water wave problem in 3-D
TL;DR: In this paper, the authors considered the 2D full nonlinear water wave problem in Sobolev spaces and showed that the motion of the interface separating an inviscid, incompressible, irrotational fluid from a region of zero density in 3D space is well-posed.
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Well-posedness of the water-waves equations
TL;DR: In this article, the authors restrict their attention to the case when the surface is a graph parameterized by a function?(?,X), where t denotes the time variable and X = (Xi,...,Xd) Rd the horizontal spatial variables.
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Global wellposedness of the 3-D full water wave problem
TL;DR: In this paper, the authors consider the problem of global in time existence and uniqueness of solutions of the 3D infinite depth full water wave problem, in the setting that the interface tends to the horizontal plane, the velocity and acceleration on the interface tend to zero at spatial infinity.
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Global well-posedness of the 3-D full water wave problem
TL;DR: In this paper, the authors consider the problem of global in time existence and uniqueness of solutions of the 3D infinite depth full water wave problem and show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders.
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On the free boundary problem of three‐dimensional incompressible Euler equations
TL;DR: In this paper, the motion of a general inviscid, incompressible fluid with a free interface that separates the fluid region from the vacuum was considered in 3D space and the local well-posedness of the free boundary problem in Sobolev space was proved.