$$\bex \p_3\pi\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{12}{7},\quad \frac{12}{7}\leq q\leq 4. \eex$$
[Papers]MHD, $\p_3\pi$, Lebesgue space [Cao-Wu, JDE, 2010]

$$\bex \p_3\pi\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{12}{7},\quad \frac{12}{7}\leq q\leq 4. \eex$$