Harmonic solutions and weak solutions of two-dimensional rotational incompressible Euler equations

Abstract

In this paper, two families of exact solutions to two-dimensional incompressible rotational Euler equations are constructed by connecting the Euler equations with the Laplace equation via a stream function. The constituent solutions in the first family are smooth, orthogonal, and conjugate harmonic solutions, while their constituent velocities are nonlinear with respect to the spatial variables. The second family are weak solutions in the distribution sense.

Keywords

• Euler equations
• Laplace equation
• Weak solutions