[Papers]NSE, $u$, Lorentz space [Sohr, JEE, 2001]

简介: $$\bex \bbu\in L^{p,r}(0,T;L^{q,\infty}(\bbR^3)),\quad\frac{2}{p}+\frac{3}{q}=1,\quad 3

$$\bex \bbu\in L^{p,r}(0,T;L^{q,\infty}(\bbR^3)),\quad\frac{2}{p}+\frac{3}{q}=1,\quad 3<q<\infty,\quad 2<p<r<\infty, \eex$$ or $$\bex \sen{\bbu}_{L^{p,\infty}(0,T;L^{q,\infty}(\bbR^3))}\leq \ve,\quad \frac{2}{p}+\frac{3}{q}=1,\quad 3<q<\infty,\quad 2<p<\infty, \eex$$

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$$\bex \sen{\pi}_{L^{s,\infty}(0,T;L^{q,\infty}(\bbR^3))} \leq \ve_*, \eex$$ with $$\bex \frac{2}{s}+\frac{3}{q}=2,\quad \frac{5}{2}\leq q\leq 3.
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[Papers]NSE, $u_3$, Lebesgue space [Zhou-Pokorny, Nonlinearity, 2009]
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[Papers]NSE, $\n u_3$, Lebesgue space, [Pokorny, EJDE, 2003; Zhou, MAA, 2002]
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[Papers]NSE, $\p_3u$, Lebesgue space [Penel-Pokorny, AM, 2004]
$$\bex \p_3\bbu\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{3}{2},\quad 2\leq q\leq \infty. \eex$$
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[Papers]NSE, $u_3$, Lebesgue space [Cao-Titi, IUMJ, 2008]
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