Ill-Posedness for the Nonlinear Davey-Stewartson Equation |
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Authors: | Shen Caixia Guo Boling |
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Affiliation: | aFaculty of Science, University of Jiang Su, Zhenjiang 212013, China;bInstitute of Applied Physics and Computational Mathematics, Beijing 100088, China |
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Abstract: | The nonlinear D-S equations on Rd, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be ill-posed in the Sobolev space Hs whenever the exponent s is lower than that predicted by scaling or Galilean invariance, or when the regularity is too low to support distributional solutions. Authors analyze a class of solutions for which the zero-dispersion limit provides good approximations. |
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Keywords: | The Davey-Stewartson equation the Cauchy problem ill-posedness |
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