On the definition and properties of p-superharmonic functions.
In this paper we prove the existence of a weak solution for a given semilinear singular real hyperbolic system.
We study the -dimensional Boussinesq system with dissipation and diffusion generalized in terms of fractional Laplacians. In particular, we show that given the critical dissipation, a solution pair remains smooth for all time even with zero diffusivity. In the supercritical case, we obtain component reduction results of regularity criteria and smallness conditions for the global regularity in dimensions two and three.
We prove that the one-dimensional Euler–Poisson system driven by the Poisson forcing together with the usual -law pressure, , admits global solutions for a large class of initial data. Thus, the Poisson forcing regularizes the generic finite-time breakdown in the -system. Global regularity is shown to depend on whether or not the initial configuration of the Riemann...
In this paper we prove the global well-posedness of the two-dimensional Boussinesq system with zero viscosity for rough initial data.