Uniform in <i>N</i> estimates for a Bosonic system of HartreeāFockāBogoliubov type
Uniform in <i>N</i> estimates for a Bosonic system of HartreeāFockāBogoliubov type
We prove local in time, uniform in N, estimates for the solutions Ļ, Ī, and Ī of a coupled system of HartreeāFockāBogoliubov type with interaction potential vN(xāy)=N3Ī²v(NĪ²(xāy)), with Ī²<1 and v a Schwartz function (satisfying additional technical requirements). The initial conditions are general functions in a Sobolev-type space, and the ā¦