## Rocky Mountain Journal of Mathematics

- Rocky Mountain J. Math.
- Volume 48, Number 8 (2018), 2595-2623.

### The Cauchy problem for the degenerate convective Cahn-Hilliard equation

#### Abstract

In this paper, we study the degenerate convective Cahn-Hilliard equation, which is a special case of the general convective Cahn-Hilliard equation with $M(u,\nabla u)=diag(0,1,\ldots ,1)$. We obtain the uniform a priori decay estimates of a solution by use of the long-short wave method and the frequency decomposition method. We prove the existence of the unique global classical solution with small initial data by establishing the uniform estimates of the solution. Decay estimates are also discussed.

#### Article information

**Source**

Rocky Mountain J. Math., Volume 48, Number 8 (2018), 2595-2623.

**Dates**

First available in Project Euclid: 30 December 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.rmjm/1546138823

**Digital Object Identifier**

doi:10.1216/RMJ-2018-48-8-2595

**Mathematical Reviews number (MathSciNet)**

MR3894995

**Zentralblatt MATH identifier**

06999276

**Subjects**

Primary: 35K25: Higher-order parabolic equations

Secondary: 35A09: Classical solutions 35K59: Quasilinear parabolic equations

**Keywords**

Convective Cahn-Hilliard equation frequency decomposition existence Green's function method

#### Citation

Liu, Aibo; Liu, Changchun. The Cauchy problem for the degenerate convective Cahn-Hilliard equation. Rocky Mountain J. Math. 48 (2018), no. 8, 2595--2623. doi:10.1216/RMJ-2018-48-8-2595. https://projecteuclid.org/euclid.rmjm/1546138823