The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
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DOI：
10.1007/s002090100332
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发表时间：
2002-12
影响因子：
0.8
通讯作者：
H. Kozono;T. Ogawa;Y. Taniuchi
中科院分区：
文献类型：
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作者：
H. Kozono;T. Ogawa;Y. Taniuchi
在对数形式的Besov空间Brezis-Gallouet-Wainger和Beale-Kato-Majda中证明了临界Sobolev不等式.作为这些不等式的应用，讨论了Navier-Stokes方程、Euler方程在临界条件下的正则性问题以及球调和映射的梯度流问题。即在Besov空间上改进了Serrin-Ohyama型正则性准则。
We show the critical Sobolev inequalities in the Besov spaces with the logarithmic form such as Brezis-Gallouet-Wainger and Beale-Kato-Majda. As an application of those inequalities, the regularity problem under the critical condition to the Navier-Stokes equations, the Euler equations inand the gradient flow to the harmonic map to the sphere are discussed. Namely the Serrin-Ohyama type regularity criteria are improved in the terms of the Besov spaces.