TY - JOUR

T1 - On the analyticity and the almost periodicity of the solution to the Euler equations with non-decaying initial velocity

AU - Sawada, Okihiro

AU - Takada, Ryo

N1 - 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 Universität Darmstadt. The second author acknowledges the support by International Research Training Group 1529 during his stay at Technische Universität Darmstadt. He is also partly supported by Research Fellow of the Japan society for Promotion of Science for Young Scientists.

PY - 2011/4/1

Y1 - 2011/4/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jfa.2010.12.011

DO - 10.1016/j.jfa.2010.12.011

M3 - Article

AN - SCOPUS:78651455983

SN - 0022-1236

VL - 260

SP - 2148

EP - 2162

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 7

ER -