Zhichun Zhai

most citedWell-posedness and regularity of generalized Navier-Stokes equations in some Critical

Q -

spaces

4 citations · 9 across the 8 of their papers we have counts for

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7 papers · 1 filter

math.AP2009

Riesz transforms on Q-type spaces with application to quasi-geostrophic equation

Pengtao Li, Zhichun Zhai

In this paper, we prove the boundedness of Riesz transforms $\partial_{j} (- Δ)^{- 1/2}$ ( $j = 1, 2, ..., n$ ) on the Q-type spaces $Q_{α}^{β} (R^{n})$ . As an application, we get the we…

math.AP2009

Well-posedness for fractional Navier-Stokes equations in critical spaces close to $B ˙_{\infty, \infty}^{- (2 β - 1)} (R^{n})$

Zhichun Zhai

In this paper, we prove the well-posedness for the fractional Navier-Stokes equations in critical spaces $G_{n}^{- (2 β - 1)} (R^{n})$ and $B M O^{- (2 β - 1)} (R^{n}) .$ Both…

math.AP2009★ 1 cited

Carleson measure problems for parabolic Bergman spaces and homogeneous Sobolev spaces

Zhichun Zhai

Let $b_{α}^{p} (R_{+}^{1 + n})$ be the space of solutions to the parabolic equation $\partial_{t} u + (- △)^{α} u = 0$ $(α \in (0, 1])$ having finite $L^{p} (R_{+}^{1 + n})$ …

math.AP2009★ 3 cited

Generalized Naiver-Stokes equations with initial data in local $Q$ -type spaces

Pengtao Li, Zhichun Zhai

In this paper, we establish a link between Leray mollified solutions of the three-dimensional generalized Naiver-Stokes equations and mild solutions for initial data in the adheren…

math.AP2009★ 4 cited

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

Pengtao Li, Zhichun Zhai

We 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…

math.AP2009★ 1 cited

Strichartz type estimates for fractional heat equations

Zhichun Zhai

We obtain Strichartz estimates for the fractional heat equations by using both the abstract Strichartz estimates of Keel-Tao and the Hardy-Littlewood-Sobolev inequality. We also pr…

Riesz transforms on Q-type spaces with application to quasi-geostrophic equation

Well-posedness for fractional Navier-Stokes equations in critical spaces close to B˙∞,∞−(2β−1)​(Rn)

Carleson measure problems for parabolic Bergman spaces and homogeneous Sobolev spaces

Generalized Naiver-Stokes equations with initial data in local Q-type spaces

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

Strichartz type estimates for fractional heat equations

Well-posedness for fractional Navier-Stokes equations in critical spaces close to $B ˙_{\infty, \infty}^{- (2 β - 1)} (R^{n})$

Generalized Naiver-Stokes equations with initial data in local $Q$ -type spaces

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