Well-posedness in Sobolev spaces of the full water wave problem in 3-D
Tóm tắt
We consider the motion of the interface of a 3-D inviscid, incompressible, irrotational water wave, with air region above water region and surface tension zero. We prove that the motion of the interface of the water wave is not subject to Taylor instability, as long as the interface separates the whole 3-D space into two simply connected
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Beale, J. Thomas, 1993, Growth rates for the linearized motion of fluid interfaces away from equilibrium, Comm. Pure Appl. Math., 46, 1269, 10.1002/cpa.3160460903
Brackx, F., 1982, Clifford analysis, 76
R. E. Caflisch, Mathematical Analysis of Vortex Dynamics, Mathematical Aspects of Vortex Dynamics, edited by R. E. Caflisch, Philadelphia : Society for Industrial and Applied Mathematics 1988.
Coifman, R. R., 1982, L’intégrale de Cauchy définit un opérateur borné sur 𝐿² pour les courbes lipschitziennes, Ann. of Math. (2), 116, 361, 10.2307/2007065
Coifman, R. R., 1983, La solution des conjecture de Calderón, Adv. in Math., 48, 144, 10.1016/0001-8708(83)90084-1
Craig, Walter, 1985, An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits, Comm. Partial Differential Equations, 10, 787, 10.1080/03605308508820396
Birkhoff, Garrett, 1962, Helmholtz and Taylor instability, 55
Gilbarg, David, 1983, Elliptic partial differential equations of second order, 224, 2, 10.1007/978-3-642-61798-0
Gilbert, John E., 1991, Clifford algebras and Dirac operators in harmonic analysis, 26, 10.1017/CBO9780511611582
Hou, Thomas Y., 1996, Well-posedness of linearized motion for 3-D water waves far from equilibrium, Comm. Partial Differential Equations, 21, 1551, 10.1080/03605309608821238
Kano, Tadayoshi, 1979, Sur les ondes de surface de l’eau avec une justification mathématique des équations des ondes en eau peu profonde, J. Math. Kyoto Univ., 19, 335, 10.1215/kjm/1250522437
Kenig, Carlos E., 1986, Elliptic boundary value problems on Lipschitz domains, 131
Kenig, Carlos E., 1994, Harmonic analysis techniques for second order elliptic boundary value problems, 83, 10.1090/cbms/083
Mitrea, Marius, 1994, Clifford wavelets, singular integrals, and Hardy spaces, 1575, 10.1007/BFb0073556
Mizohata, Sigeru, 1973, The theory of partial differential equations
Murray, Margaret A. M., 1985, The Cauchy integral, Calderón commutators, and conjugations of singular integrals in 𝑅ⁿ, Trans. Amer. Math. Soc., 289, 497, 10.2307/2000250
Nalimov, V. I., 1974, The Cauchy-Poisson problem, Dinamika Splo\v{s}n. Sredy, 104
Shinbrot, Marvin, 1976, The initial value problem for surface waves under gravity. I. The simplest case, Indiana Univ. Math. J., 25, 281, 10.1512/iumj.1976.25.25023
Stein, Elias M., 1971, Introduction to Fourier analysis on Euclidean spaces
Stoker, J. J., 1957, Water waves: The mathematical theory with applications
Hopkins, Charles, 1939, Rings with minimal condition for left ideals, Ann. of Math. (2), 40, 712, 10.2307/1968951
Verchota, Gregory, 1984, Layer potentials and regularity for the Dirichlet problem for Laplace’s equation in Lipschitz domains, J. Funct. Anal., 59, 572, 10.1016/0022-1236(84)90066-1
Wu, Sijue, 1997, Well-posedness in Sobolev spaces of the full water wave problem in 2-D, Invent. Math., 130, 39, 10.1007/s002220050177
Yosihara, Hideaki, 1982, Gravity waves on the free surface of an incompressible perfect fluid of finite depth, Publ. Res. Inst. Math. Sci., 18, 49, 10.2977/prims/1195184016
Andreev, V. K., 1992, {\cyr Usto\u{i}} {\cyr chivost\cprime neustanovivshikhsya dvizheni\u{i}} {\cyr zhidkosti so svobodno\u{i}} {\cyr granitse\u{i}}