Analyticity for a class of nonlocal Kuramoto-Sivashinsky equations arising in interfacial electrohydrodynamics

In this article, we study the analyticity properties of solutions of the nonlocal Kuramoto-Sivashinsky equations, u(t) + uu(x) + u(xx) + u(xxxx) - mu(Ho partial derivative(x))(p)[u] = 0, defined on 2 pi-periodic intervals, where.. is a positive constant; mu is a nonnegative constant; p is an arbitrary but fixed real number in the interval [3, 4); and (Ho partial derivative(x))(p) is an operator defined by its symbol in Fourier space, with. be the Hilbert transform. We establish spatial analyticity in a strip around the real axis for the solutions of such equations, which possess universal attractors. Also, a lower bound for the width of the strip of analyticity is obtained.