Global solutions to semirelativistic Hartree equations
Preprint Series # 813
Cho, Yonggeun and Ozawa, Tohru Global solutions to semirelativistic Hartree equations. (2006);
We consider initial value problems for the semirelativistic Hartree
equations with cubic convolution nonlinearity $F(u) = (V * |u|^2)u$.
Here $V$ is a sum of two Coulomb type potentials. Under a specified
decay condition and a symmetric condition for the potential $V$ we
show the global existence and scattering of solutions.
|Uncontrolled Keywords:||semirelativistic Hartree equations, global existence,
scattering, Coulomb type potentials|
|Subjects:||35-xx PARTIAL DIFFERENTIAL EQUATIONS|