Let's say I have an equation of the form $\Delta A = J$ where $J=u\nabla u + A|u|^2$. Then I could simply infer from Hardy-Littlewood-Sobolev and Hölder that $$\|A\|_6 \leq \|J\|_{6/5} \leq \|u\|_3\|\nabla u\|_2 +\|A\|_6 \|u\|_3^2$$ and then from Sobolev $$\cdots \leq \|u\|_{H^1}^2 + \|A\|_6 \|u\|_{H^1}^2$$ Can I somehow infer from that that $\|A\|_6$ is controlled by some norm of $u$?
2026-04-14 07:08:06.1776150486
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