Remarks on asymptotic behaviors of strong solutions to a viscous Boussinesq system |
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Authors: | Shangkun Weng |
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Institution: | Pohang Mathematics Institute, Pohang University of Science and Technology, Nam‐Gu Pohang, Gyungbuk 790‐784, Korea |
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Abstract: | In this paper, we first address the space‐time decay properties for higher‐order derivatives of strong solutions to the Boussinesq system in the usual Sobolev space. The decay rates obtained here are optimal. The proof is based on a parabolic interpolation inequality, bootstrap argument, and some weighted estimates. Secondly, we present a new solution integration formula for the Boussinesq system, which will be employed to establish the existence of strong solutions for small initial data in some scaling invariant function spaces. The smallness conditions are somehow weaker than those presented by Brandolese and Schonbek. We further investigate the asymptotic profiles and decay properties of these strong solutions. Copyright © 2016 John Wiley & Sons, Ltd. |
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Keywords: | Boussinesq equations integration formula scaling invariant asymptotic profile weighted estimates |
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