On the Cauchy-problem for generalized Kadomtsev-Petviashvili-II equations
The Cauchy-problem for the generalized Kadomtsev-Petviashvili-II equation $$ u_t + u_{xxx} + partial_x^{-1}u_{yy}= (u^l)_x, quad l ge 3, $$ is shown to be locally well-posed in almost critical anisotropic Sobolev spaces. The proof combines local smoothing and maximal function estimates as we...
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| Format: | Article |
| Language: | English |
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Texas State University
2009-07-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2009/82/abstr.html |