On well-posedness and decay of Active model B

We study the well-posedness and decay estimates of Cauchy problem for Active model B in R3. First, based on the higher-order norm estimates of solutions and the mollifier technique, we obtain the local existence of unique strong solution. Then, by using pure energy method, one proves the global well-posedness and time decay estimates, provided that the H3/2-norm of initial data is sufficiently small.