相关论文: Infinite energy solutions for the Cahn-Hilliard eq…

We study the infinite-energy solutions of the Cahn-Hilliard equation in the whole 3D space in uniformly local phase spaces. In particular, we establish the global existence of solutions for the case of regular potentials of arbitrary…

Our aim in this paper is to study the Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. In particular, we prove, owing to proper approximations of the singular potential and a suitable notion of variational…

The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of the order parameter multiplied by an inertial coefficient…

In this note, we consider the nonlocal Cahn-Hilliard equation with constant mobility and singular potential in three dimensional bounded and smooth domains. Given any global solution (whose existence and uniqueness are already known), we…

We address, in a three-dimensional spatial setting, both the viscous and the standard Cahn-Hilliard equation with a nonconstant mobility coefficient. As it was shown in J.W. Barrett and J.W. Blowey, Math. Comp., 68 (1999), 487-517, one…

We consider the Cahn-Hilliard equation on manifolds with conical singularities and prove existence of global attractors in higher order Mellin-Sobolev spaces with asymptotics. We also show convergence of solutions in the same spaces to an…

We consider a Cahn-Hilliard equation which is the conserved gradient flow of a nonlocal total free energy functional. This functional is characterized by a Helmholtz free energy density, which can be of logarithmic type. Moreover, the…

Here we consider a Cahn-Hilliard-Navier-Stokes system characterized by a nonlocal Cahn-Hilliard equation with a singular (e.g., logarithmic) potential. This system originates from a diffuse interface model for incompressible isothermal…

The paper gives a comprehensive study of infinite-energy solutions and their long-time behavior for semi-linear weakly damped wave equations in $\mathbb{R}^3$ with quintic nonlinearities. This study includes global well-posedness of the…

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 $\R^3$ started in our previous paper and verify that under the natural assumptions on…

We study the Euler equations with the so-called Ekman damping in the whole 2D space. The global well-posedness and dissipativity for the weak infinite energy solutions of this problem in the uniformly local spaces is verified based on the…

We consider a class of six-order Cahn-Hilliard equations with logarithmic type potential. This system is closely connected with some important phase-field models relevant in different applications, for instance, the functionalized…

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 non-linearity of the sub-quintic growth rate. Moreover, the dissipativity and the existence of a…

A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard…

This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\mathbb{R}^3$ with fractional damping of the form $(-\Delta_x+1)^\frac{1}{2}\partial_t u$. The work extends previously known…

We consider the nonlocal Cahn-Hilliard equation with singular (logarithmic) potential and constant mobility in three-dimensional bounded domains and we establish the validity of the instantaneous strict separation property. This means that…

This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a characteristic growth at infinity we…

We investigate the long-time behavior of a nonlocal Cahn-Hilliard equation in a bounded domain $\Omega\subset\mathbb{R}^d$ $(d\in\{2,3\})$, subject to a kinetic rate-dependent nonlocal dynamic boundary condition. The kinetic rate $1/L$,…

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a…

We prove the existence of infinite energy global solutions of the cubic wave equation in dimension greater than 3. The data is a typical element on the support of suitable probability measures.