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[Papers]NSE, $\n u_3$, Lebesgue space, [Pokorny, EJDE, 2003; Zhou, MAA, 2002]
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[Papers]NSE, $\n u_3$, Lebesgue space, [Pokorny, EJDE, 2003; Zhou, MAA, 2002]
$$\bex \n u_3\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{3}{2},\quad 2\leq q\leq \infty. \eex$$…
[Papers]MHD, $\p_3\pi$, Lebesgue space [Zhang-Li-Yu, JMAA, 2013]
$$\bex \p_3\pi\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=2,\quad \frac{3}{2}\leq q\leq 3. \eex$$…
[Papers]MHD, $\p_3\pi$, Lebesgue space [Jia-Zhou, JMAA, 2012]
$$\bex \p_3\pi\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=2,\quad 3\leq q\leq \infty. \eex$$…
[Papers]MHD, $\p_3\pi$, Lebesgue space [Cao-Wu, JDE, 2010]
$$\bex \p_3\pi\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{12}{7},\quad \frac{12}{7}\leq q\leq 4. \eex$$…
[Papers]NSE, $u_3$, Lebesgue space [Jia-Zhou, NARWA, 2014]
$$\bex u_3\in L^\infty(0,T;L^\frac{10}{3}(\bbR^3)). \eex$$…
[Papers]NSE, $u_3$, Lebesgue space [Zhou-Pokorny, Nonlinearity, 2009]
$$\bex u_3\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{3}{4}+\frac{1}{2q},\quad \frac{10}{3}<q\leq\infty. \eex$$…
[Papers]NSE, $u_3$, Lebesgue space [Cao-Titi, IUMJ, 2008]
$$\bex u_3\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{2}{3}+\frac{2}{3q},\quad \frac{7}{2}<q\leq \infty. \eex$$…
[Papers]NSE, $u_3$, Lebesgue space [Kukavica-Ziane, Nonlinearity, 2006]
$$\bex u_3\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{5}{8},\quad \frac{24}{5}<q\leq \infty. \eex$$…
[Papers]NSE, $u_3$, Lebesgue space [NNP, QM, 2002; Zhou, JMPA, 2005]
$$\bex u_3\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{1}{2},\quad 6< q\leq \infty. \eex$$…
[Papers]NSE, $\p_3u$, Lebesgue space [Cao, DCDSA, 2010]
$$\bex \p_3\bbu\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=2,\quad \frac{27}{16}\leq q\leq \frac{5}{2}. \eex$$…