| Abstract: |
| We will present methods of existence theory for free-surface fluid flows in the case of uniformly local Sobolev data and in the case of spatially quasiperiodic initial data. These are both instances of non-decaying, non-periodic fluid flows. Such data could arise, for instance, when making a non-periodic perturbation of a periodic flow, or when wavetrains with different, non-commensurate periodicities interact. Among the topics to be discussed are a version of the Birkhoff-Rott integral and Hilbert transform which do not require decay or periodicity, and estimates for these in uniformly local Sobolev spaces. Another potential framework to be applied is the Cauchy-Kowalevski theorem, and some interesting consequences of this in the spatially quasiperiodic setting will be discussed. |
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