@article{f4a88d45563c447b88d92ef5c3ef4d8c,

title = "On the analyticity and the almost periodicity of the solution to the Euler equations with non-decaying initial velocity",

abstract = "The Cauchy problem of the Euler equations in the whole space is considered with non-decaying initial velocity in the frame work of B∞,11. It is proved that if the initial velocity is real analytic then the solution is also real analytic in spatial variables. Furthermore, a new estimate for the size of the radius of convergence of Taylor's expansion is established. The key of the proof is to derive the suitable estimates for the higher order derivatives of the bilinear terms. It is also shown the propagation of the almost periodicity in spatial variables.",

keywords = "Almost periodicity, Analyticity, Non-decaying initial velocity, The Euler equations",

author = "Okihiro Sawada and Ryo Takada",

note = "Funding Information: The authors would like to express their sincere gratitude to Professor Hideo Kozono for his valuable suggestions and continuous encouragement. They are also grateful to Professor Matthias Hieber and Professor Reinhard Farwig for their various supports. The first author is partly supported by Alexander von Humboldt Fellowship for his stay at Technische Universit{\"a}t Darmstadt. The second author acknowledges the support by International Research Training Group 1529 during his stay at Technische Universit{\"a}t Darmstadt. He is also partly supported by Research Fellow of the Japan society for Promotion of Science for Young Scientists.",

year = "2011",

month = apr,

day = "1",

doi = "10.1016/j.jfa.2010.12.011",

language = "English",

volume = "260",

pages = "2148--2162",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "7",

}