Ground States of a Two Phase Model with Cross and Self Attractive Interactions

M. Cicalese, L. De Luca, M. Novaga, M. Ponsiglione
<span title="">2016</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pqj7exj2prhsxiakouer6gzgn4" style="color: black;">SIAM Journal on Mathematical Analysis</a> </i> &nbsp;
We consider a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, different behaviors are possible: phase mixing or phase separation with nested or disjoint phases. In the case of Coulomb interaction forces, we characterize the ground state configurations. 12 2.2. The strongly attractive case c 11 + c 22 ≤ −2 13 2.3. The weakly
more &raquo; ... ve case c 11 + c 22 > −2 16 3. The Coulomb kernel 17 3.1. Consequences of the first variation 17 3.2. The strongly attractive case c 11 + c 22 ≤ −2 18 3.3. The weakly attractive case c 11 + c 22 > −2 (preliminary results) 18 3.4. The weakly attractive case c 11 + c 22 > −2 (in dimension N = 1) 20 3.5. The weakly attractive case c 11 + c 22 > −2 (the case N ≥ 2) 21 Conclusions and perspectives 27 References 29
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