Bulletin of the American Mathematical Society

A simplified version of the abstract Cauchy-Kowalewski theorem with weak singularities

Author(s): Russel E. Caflisch
Journal: Bull. Amer. Math. Soc. 23 (1990), 495-500.
MSC (1985): Primary 35A10
MathSciNet review: 1027897
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1.: K. Asano, A note on the abstract Cauchy-Kowalewski theorem, Proc. Japan Acad. Ser. A Math. Sci. 64 (1988), 102-105. MR 966397
2.: K. Asano, Zero-viscosity limit of the incompressible Navier-Stokes equations II, preprint, 1988. MR 979500
3.: M. S. Baouendi and C. Goulaouic, Remarks on the abstract form of nonlinear Cauchy-Kovalevsky theorems, Comm. Partial Differential Equations 2 (1977), 1151- 1162. MR 481322
4.: R. E. Caflisch and O. F. Orellana, Long time existence for a slightly perturbed vortex sheet, Comm. Pure Appl. Math. 39 (1986), 807-838. MR 859274
5.: R. E. Caflisch and O. F. Orellana, Singularity formulation and ill-posedness for vortex sheets, SIAM J. Math. Anal. 20 (1988), 293-307. MR 982661
6.: R. E. Caflisch and J. Lowengrub, Convergence of the vortex method for vortex sheets, SIAM J. Numer. Anal. 26 (1989), 1060-1080. MR 1014874
7.: R. E. Caflisch, N. Ercolani, and T. Y. Hou, Singularity formation on planar vortex sheets, preprint, 1990.
8.: T. Kano and T. Nishida, Sur les ondes de surface de l'eau avec une justification mathématique des equations des ondes en eau peu profonde, J. Math. Kyoto Univ. 19 (1979), 335-370. MR 545714
9.: L. Nirenberg, An abstract form of the nonlinear Cauchy-Kowalewski theorem, J. Differential Geom. 6 (1972), 561-576. MR 322321
10.: T. Nishida, A note on a theorem of Nirenberg, J. Differential Geom. 12 (1977), 629-633. MR 512931
11.: T. Nishida, Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation, Comm. Math. Phys. 61 (1978), 119-148. MR 503305
12.: L. V. Ovsjannikov, A nonlinear Cauchy problem in a scale of Banach spaces, Sov. Math. Dokl. 12 (1971), 1497-1502. MR 285941
13.: P. Sulem, C. Sulem, C. Bardos, and U. Frisch, Finite time analyticity for the two and three dimensional Kelvin-Helmholtz instability, Comm. Math. Phys. 80 (1981), 485-516. MR 628507

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