On the analyticity and the almost periodicity of the solution to the Euler equations with non-decaying initial velocity |
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Authors: | Okihiro Sawada |
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Institution: | a Department of Mathematics, Darmstadt University of Technology, Schlossgartenstrasse 7, D-64289 Darmstadt, Germany b Mathematical Institute, Tohoku University, 6-3 Aoba, Sendai 980-8578, Japan |
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Abstract: | The Cauchy problem of the Euler equations in the whole space is considered with non-decaying initial velocity in the frame work of . 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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Keywords: | The Euler equations Analyticity Almost periodicity Non-decaying initial velocity |
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