On global attractors of multivalued semiflows generated by the 3D Bénard system (Q693007)

The authors study the three-dimensional Bénard system and show the existence of continuous solutions with respect to the second component. By introducing the multivalued semiflow on the whole phase space and the notion of \(\phi\)-attraction, the authors show the existence of a global \(\phi\)-attractor for the weak-strong topology. As a particular case, the authors obtain the existence in the sense of weak topology for the 3D incompressible Navier-Stokes equations. Their results extend previous ones.