LDP under the weak Kato hypothesis

The paper studies the large deviations principle for the two-dimensional Navier–Stokes system in a bounded domain, with Kato conditions controlling the inviscid limit and with forcing in the relevant $L^2$ space. The weak Kato condition is the condition referred to as weak kato cond, while the strong Kato hypothesis is the hypothesis referred to as strong kato hp in the main large-deviations theorem.

LDP under the weak Kato hypothesis. The statement of the main large-deviations theorem holds true if the strong Kato hypothesis is replaced with the weak Kato condition.

This would strengthen the paper's result by showing that the strong Kato assumption is unnecessary for the large deviations principle, at least for the zero-forcing system considered in the main theorem. The source presents this as a possible improvement, and no resolution is supplied here.