Well-posedness and regularity of generalized Navier-Stokes equations in some Critical $Q-$spaces

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dc.creatorLi, Pengtao
dc.creatorZhai, Zhichun
dc.date2009-04-21
dc.date.accessioned2026-07-07T13:06:53Z
dc.date.available2026-07-07T13:06:53Z
dc.descriptionWe study the well-posedness and regularity of the generalized Navier-Stokes equations with initial data in a new critical space $Q_{α;\infty}^{β,-1}(\mathbb{R}^{n})=\nabla\cdot(Q_α^β(\mathbb{R}^{n}))^{n}, β\in({1/2},1)$ which is larger than some known critical homogeneous Besov spaces. Here $Q_α^β(\mathbb{R}^{n})$ is a space defined as the set of all measurable functions with $$\sup(l(I))^{2(α+β-1)-n}\int_{I}\int_{I}\frac{|f(x)-f(y)|^{2}}{|x-y|^{n+2(α-β+1)}}dxdy<\infty$$ where the supremum is taken over all cubes $I$ with the edge length $l(I)$ and the edges parallel to the coordinate axes in $\mathbb{R}^{n}.$ In order to study the well-posedness and regularity, we give a Carleson measure characterization of $Q_α^β(\mathbb{R}^{n})$ by investigating a new type of tent spaces and an atomic decomposition of the predual for $Q_α^β(\mathbb{R}^{n}).$ In addition, our regularity results apply to the incompressible Navier-Stokes equations with initial data in $Q_{α;\infty}^{1,-1}(\mathbb{R}^{n}).$
dc.description48 pages
dc.identifierhttps://arxiv.org/abs/0904.3271
dc.identifierhttp://arxiv.org/abs/0904.3271
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227921
dc.subjectAnalysis of PDEs
dc.titleWell-posedness and regularity of generalized Navier-Stokes equations in some Critical $Q-$spaces
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