On the analyticity of the flow map for the AHT equations

The AHT equation is a nonlinear and nonlocal vectorial transport equation which was introduced by Angenent, Haker, and Tannenbaum [SIAM J. Math. Anal. 35 (2003), pp. 61–97] in optimal transport theory. For this equation, classical solutions are known to exist at least locally in time, and a flow map can thus be uniquely associated with these solutions. In this paper we consider the case where the equation is set in a bounded domain with an analytic boundary and we prove that the flow map is analytic with respect to time.