Global Regularity for a Model of Inhomogeneous Three-dimensional Navier-Stokes Equations
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摘要: 考虑一个非均质三维Navier-Stokes方程模型,借助能量方法、Littlewood-Paley仿积分解技巧和Sobolev嵌入定理研究解的整体正则性. 用-D2u近似替代经典非均质Navier-Stokes方程中的耗散项Δu,得到一个新的Navier-Stokes方程模型,其中D是一个傅里叶乘子,其特征是m(ξ)=|ξ|5/4,对于任意小的正常数ε和δ,当初值(ρ0,u0)∈H3/2+ε×Hδ时,证明了该模型解的爆破准则和整体正则性.
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关键词:
- 非均质Navier-Stokes方程 /
- Littlewood-Paley仿积分解 /
- 整体正则性 /
- 爆破准则
Abstract: A model of inhomogeneous three-dimensional Navier-Stokes equations was studied in this paper. By using the energy method, Littlewood-Paley paraproduct decomposition techniques and Sobolev embedding theorem study of the global regularity of solutions were adopted. The dissipative term Δu in the classical inhomogeneous Navier-Stokes equations is replaced by -D2u and a new Navier-Stokes equations model was obtained, where D was a Fourier multiplier whose symbol is m(ξ)=|ξ|5/4. Blow-up criterion and global regularity of this model were proved for the initial data (ρ0,u0)∈H3/2+ε×Hδ, where ε and δ are arbitrary small positive constants. -
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