On the existence of \(L^{p}\) solutions of the magnetohydrodynamic equations in a bounded domain (Q1400284)

The aim of this paper is to show the global existence of the nonstationary magnetohydrodynamic equations in \(L^{3}\) for \(L^{3}\) initial data in the vicinity of the trivial solutions without any regularity assumptions on the initial data and study the asymptotic behaviour when \(t\) tends to infinity. The considered domain is supposed to be bounded in \(\mathbb{R}^{3}\) having also as boundary a sufficiently smooth compact hypersurface while the non-slip boundary condition is accomplished with the fulfillment of the perfect conducting wall condition by the magnetic field vector.