On the differentiability of solutions of the liminal dissipative equation

There is established the conditions under which the solutions of the liminal dissipative equation have third derivatives with respect to the spatial variables. As principal conditions for a prolongation of solutions are formulated for the second derivatives, the equation for the second derivative of a solution to considered problem is constructed. The peculiarity of this equation is that its in the extended characteristic system has a convenient to deducing of global estimates form.