The manuscript seems to infer that regularity is a necessary condition for the well-posedness of the coupled problem. Therefore, the phrasing "the underlying coupled problem might not “obey regularity” or could even be ill-posed" is somehow counter-intuitive to me, particularly the word "even". From my understanding of the manuscript, a coupled problem that does not obey regularity is already expected to be ill-posed, precisely because it is not regular. So why insisting on "or it could even be ill-posed", as if this consisted in a stronger statement?

Sorry about this obscure comment, that's a leftover from earlier drafting that should have been removed. I was thinking about eq. 8 in itself probably having a few terms keeping the coupled problem from being well-posed. At least because $C_H$ tends to not be a regular function of the solution. Potentially also the lack of surface currents representation (although that might just be an issue for momentum fluxes, not heat ones). But it’s not the point of the manuscript – please feel free to ignore this.

Sorry, wrong line numbering. The year is indeed there L. 318. I would just also repeat the year anytime a date is mentioned, e.g. L. 321 and L. 405.