An alternative proof of Lq-Lr estimates of the Oseen semigroup in higher dimensional exterior domains
An alternative proof of Lq-Lr estimates of the Oseen semigroup in higher dimensional exterior domains
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高维外部域中 Oseen 半群的 Lq-Lr 估计的另一种证明
DOI：
10.1007/s42985-021-00086-8
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Toshiaki Hishida
中科院分区：
文献类型：
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作者：
Toshiaki Hishida
-Osee半群内维外部域的衰减估计由Kobayashi和Shibata(Math Ann 310：1-45,1998)()，Enomoto和Shibata(数学流体力学杂志7：339-367,2005)()和Maekawa(J Inst Math Jussieu，2019年，https://doi.org/10.1017/s1474748019000355)()很好地建立。最近，作者(Hishida在Math Ann 372：915-949,2018，Arch Ratio Mech anal238：215-254,2020)对三维外部区域中的广义Osee演化算子证明了同样的结果，其中考虑了刚体的旋转和平移，而且平移和角速度都可以是时间相关的。如果没有非自主特征和旋转，在那里开发的方法可以大大简化。因此，不依赖于预解式的分析，就可以得到Oseen半群的衰变估计的另一种简短证明，该论点也适用于。因此，我认为提出的证据将值得在这里发表。
–decay estimates of the Oseen semigroup inn-dimensional exterior domains were well established by Kobayashi and Shibata (Math Ann 310:1–45, 1998) (), Enomoto and Shibata (J Math Fluid Mech 7:339–367, 2005) () and Maekawa (J Inst Math Jussieu, 2019, https://doi.org/10.1017/s1474748019000355) (). The same result has been recently proved by the present author (Hishida in Math Ann 372:915–949, 2018, Arch Ration Mech Anal 238:215–254, 2020) for a generalized Oseen evolution operator in 3-dimensional exterior domains, where rotation as well as translation of a rigid body is taken into account and, moreover, both translational and angular velocities can be time-dependent. The approach developed there can be considerably simplified if both the non-autonomous character and rotation are absent. As a consequence, an alternative short proof of decay estimates of the Oseen semigroup can be available without relying on analysis of the resolvent and the argument works foras well. I thus believe that the presentation of the proof would be worth publishing here.