# On Blow-up Profile of Ground States of Boson Stars with External Potential

@article{Nguyen2017OnBP, title={On Blow-up Profile of Ground States of Boson Stars with External Potential}, author={D. Nguyen}, journal={Journal of Statistical Physics}, year={2017}, volume={169}, pages={395-422} }

We study minimizers of the pseudo-relativistic Hartree functional $${\mathcal {E}}_{a}(u):=\Vert (-\varDelta +m^{2})^{1/4}u\Vert _{L^{2}}^{2}+\int _{{\mathbb {R}}^{3}}V(x)|u(x)|^{2}\mathrm{d}x-\frac{a}{2}\int _{{\mathbb {R}}^{3}}(\left| \cdot \right| ^{-1}\star |u|^{2})(x)|u(x)|^{2}\mathrm{d}x$$Ea(u):=‖(-Δ+m2)1/4u‖L22+∫R3V(x)|u(x)|2dx-a2∫R3(·-1⋆|u|2)(x)|u(x)|2dx under the mass constraint $$\int _{{\mathbb {R}}^3}|u(x)|^2\mathrm{d}x=1$$∫R3|u(x)|2dx=1. Here $$m>0$$m>0 is the mass of particles and… CONTINUE READING

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