DYNAMICS OF BROWNIAN PARTICLES IN A POTENTIAL

Let f(x,t) be the density of a cloud of particles, and T(x,t) the temp erature at x is an element of R-d at time t. Let (f) over circle is an element of L-1 (R-d) boolean AND L-p(R-d) and (T) over circle, measur able uniformly positive and exponentially bounded in R-d, be given. We study the coupled system partial derivative f/partial derivative t = div kappa(del f + f del V/T), partial derivative T/partial derivative t = kappa' partial derivative(2)T/partial derivative x(2) + kappa del V . (del f + f del V/T), with initial data f(x,0) = (f) over circle(x) and T(x,0) = (T) over circle(x). We show that there is a unique solut ion for small times if the conditions p > d, del V is an element of L- infinity and Delta V is an element of L-infinity hold. (C) 1997 Americ an Institute of Physics.