| Abstract: |
| We consider the system of compressible Euler equations augmented with nonlocal term
associated to a Riesz potential. This system emerges as a critical point of an action functional. Also it is
equipped with a stress tensor that may be expressed in two distinct representations and gives rise to an
associated bilinear fractional integral operator. We establish a uniform estimate for a bilinear fractional
integral operator via restricted weak-type endpoint estimates and Marcinkiewicz interpolation. The
estimate leads to integrability analysis of the associated stress-tensor. In addition, using the theory of
compensated integrability it yields a gain in integrability for finite-energy solutions. Finally, for smooth
periodic solutions of the reformulated system, we derive a stability result (joint work with N. Alves
(KAUST) and L. Grafakos (Univ. of Missouri)). |
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