| Abstract: |
| It has been recently shown that the classical interpolation inequalities due to Ladyzhenskaya and Gagliardo-Nirenberg can be refined by using weak $L^p$-norms. The goal of the talk is to present further refinements via general Lorentz spaces. We provide interpolation inequalities in Sobolev-Lorentz spaces of arbitrary orders, as special cases of more general results on Triebel-Lizorkin-Lorentz spaces. Then as an application, we study global weak solutions to a Stokes-Magneto system with fractional diffusions. |
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