5 problems

Let $h$ solve the thin-film equation with no-slip mobility in a domain whose contact point is $x=s(t)$, with $h=0$ at the contact line. The no-slip condition is the condition impos…

Finite dissipation implies fixed support. Then $s(t)=s_0$ is constant on $(0,T)$. Under the stated regularity and finite-dissipation assumptions, the conjecture gives a precise mat…

Consider the thin-film contact-line problem with prescribed contact angle, where the mobility exponent is $n=3$. Prescribed-angle ill-posedness conjecture. The contact line problem…

Existence and uniqueness conjecture. There exists a unique solution to equation with the contact-line conditions and.

Let $\beta(t)=h_{xx}|_{x=0}$ and let $V(t)$ denote the variables arising in the reduced dynamical model for the contact line. The conjectured finite-time blow-up occurs as…