LOWER BOUNDS FOR THE BLOWUP RATE OF SOLUTIONS OF THE ZAKHAROV EQUATION IN DIMENSION-2

We consider the blowup solution (u, n, v)(t) of the Zakharov equations [GRAPHICS] where u :R(2) --> C, n: R(2.) --> R, v: R(2) --> R(2) in t he energy space H-1 = {(u, n, v) is an element of H-1 x L(2) X L(2)}. We show that there is a constant c depending on the L(2)-norm of u(0) such that \(u, n, v)(t)\H-1 greater than or equal to\del u(t)\(L)2 gre ater than or equal to c/(T - t)' where T is the blowup time. We check that this estimate is optimal and give further applications. (C) 1996 John Wiley & Sons, Inc.