Geodesic
Evolution flow and ground states for fractional Schrödinger-Hartree equations
Mathematics and Education in Mathematics, Tome 50 (2021), pp. 45-54.

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We consider the fractional Schr¨odinger–Hartree type equations and focus our study on one particular case: the half-wave equation with nonlocal Hartree type interaction terms. The results we present can be divided in the following main topics:a) existence, asymptotic properties of ground states and their linear stability/instability;b) existence or explosion phenomena of the evolution flow with large data below/above the ground state barrier for the corresponding Cauchy problem for the half-wave equation;c) uniqueness of the ground states for the Schr¨odinger–Hartree type equations;d) blow-up for mass-critical nonlinear Schr¨odinger (NLS) equation with non-local Hartree type interaction terms
Keywords: half-wave equation, blow-up solution, ground states, 35A15, 35B44, 35C07 
@article{MEM_2021_50_a3,
     author = {Georgiev, Vladimir},
     title = {Evolution flow and ground states for fractional {Schr\"odinger-Hartree} equations},
     journal = {Mathematics and Education in Mathematics},
     pages = {45--54},
     publisher = {mathdoc},
     volume = {50},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MEM_2021_50_a3/}
}
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Georgiev, Vladimir. Evolution flow and ground states for fractional Schrödinger-Hartree equations. Mathematics and Education in Mathematics, Tome 50 (2021), pp. 45-54. http://geodesic.mathdoc.fr/item/MEM_2021_50_a3/