[Papers]MHD, $\pi$, Lorentz space [Suzuki, DCDSA, 2011]

 $$\bex \sen{\pi}_{L^{s,\infty}(0,T;L^{q,\infty}(\bbR^3))} +\sen{{\bf b}}_{L^{\gamma,\infty}(0,T;L^{\tt,\infty}(\bbR^3))}^2\leq \ve_*, \eex$$ with $$\bex \frac{2}{s}+\frac{3}{q}=2,\quad \frac{5}{2}\leq q\leq 3; \eex$$ $$\bex \frac{2}{\gamma}+\frac{3}{\tt}=1,\quad 5\leq \tt\leq 6. \eex$$ $$\bex \sen{\n \pi}_{L^{s,\infty}(0,T;L^{q,\infty}(\bbR^3))} +\sen{{\bf b}}_{L^{\gamma,\infty}(0,T;L^{\tt,\infty}(\bbR^3))}^2\leq \ve_*, \eex$$ with $$\bex \frac{2}{s}+\frac{3}{q}=3,\quad \frac{15}{11}\leq q<3; \eex$$ $$\bex \frac{2}{\gamma}+\frac{3}{\tt}=1,\quad 5\leq \tt\leq 6. \eex$$