High order convective Cahn-Hilliard type equations describe the faceting of a growing
surface, or the dynamics of phase transitions in ternary oil-water-surfactant systems. In this …

Solvability of Cauchy's problem in R 2 for subcritical quasi-geostrophic equation is
discussed here in two phase spaces; L p (R 2) with p> 2 2 α− 1 and H s (R 2) with s> 1. A …

Abstract We consider the Navier–Stokes equation (NS) in dimensions two and three as limits
of the fractional approximations. In 2-D the NS problem is critical with respect to the standard …

A growing interest in considering the “hybrid systems” of equations describing more
complicated physical phenomena was observed throughout the last 10 years. We mean …

We prove the global well-posedness of the so-called hyperbolic relaxation of the Cahn–
Hilliard–Oono equation in the whole space ℝ 3 with the nonlinearity of the sub-quintic …

In this paper we exhibit the dissipative mechanism of the Cahn–Hilliard equation in H1 (RN).
We show a weak form of dissipativity by showing that each individual solution is attracted, in …

In this paper, we continue the study of the hyperbolic relaxation of the Cahn–Hilliard–Oono
equation with the sub‐quintic non‐linearity in the whole space started in our previous paper …

This paper is concerned with the initial-boundary value problem for the hyperbolic relaxation
of the Cahn-Hilliard/Allen-Cahn equation with a proliferation term, in an arbitrary two …

This self-contained book covers the theory of semilinear equations with sectorial operator
going back to the studies of Yosida, Henry, and Pazy, which are deeply extended nowadays …

In this paper, we consider the global well-posedness of solutions for the Cauchy problem of
N-dimensional Cahn–Hilliard equation with convective term. We first construct the local …