Existence of a Class of Stretched 2D Ideal Magnetohydrodynamic Flows

We consider the existence of a class of special stretched solutions of 2D full inviscid magnetohydrodynamic equations in \({\mathbb{R}}^{2}\) ${\mathbb{R}}^2$ . The second components of the state variables have the form u₂(x, y, t) = yγ₁(x, t) + φ₁(x, t) and b₂(x, y, t) = yγ₂(x, t) + φ₂(x, t) and the first components depend on x and t only. The time global solutions of such a flow are shown to exist for positive initial values of γ₁ + γ₂ and γ₁ − γ₂.