ON NONLINEAR SCHRODINGER EQUATIONS WITH ALMOST PERIODIC INITIAL DATA

We consider the Cauchy problem of nonlinear Schrodinger equations (NLS) with almost periodic functions as initial data. We first prove that given a frequency set omega = {omega(j)}(j)(infinity) = 1, NLS is local well-posed in the algebra A omega (R) of almost periodic functions with absolutely convergent Fourier series. Then, we prove a finite time blowup result for NLS with a nonlinearity vertical bar u vertical bar(p), p is an element of 2N. This provides the first instance of finite time blowup solutions to NLS with generic almost periodic initial data.