Solutions to a phase-field model of sea ice growth

Yangxin Tang

doi:10.1186/s13661-019-1134-z

Abstract

We shall apply the phase-field method to investigate the dynamics of sea ice growth. The model consists of two parabolic equations. The existence and uniqueness of weak solutions to an initial-boundary value problem of this model is proved. Then the regularity, large-time behavior of solutions are studied, also the existence of global attractor is proved. The main technique in this article is energy method. Our existence proof is only valid in one space dimension.

Highlights

1 Introduction Due to global warming, which leads to significant climate changes and more and more frequently occurring severe weather disasters, the study of global warming seems more important than ever since sea ice has begun to melt and this makes sea level rise considerably so that some islandish countries may vanish
The application of a two-phase field model to investigation of sea ice growth presented in this paper is the first one in phase-field modeling for sea ice evolution
The mesoscopic numerical simulation of sea ice crystals growth has been studied through Voronoi dynamics during the freezing season

Summary

Introduction

Due to global warming, which leads to significant climate changes and more and more frequently occurring severe weather disasters, the study of global warming seems more important than ever since sea ice has begun to melt (see, e.g., [1,2,3]) and this makes sea level rise considerably so that some islandish countries may vanish. We will use the phasefield method in the sea ice growth, more precisely, I do theoretical analysis, regularities, and large time behavior We formulate this initial-boundary value problem in the onedimensional case and conclude the introduction by stating our main result. Using relation (4.3), we obtain, multiplying (1.8) by p and integrating by parts with respect to x over Ω, where we take the boundary condition (1.10) into account, that for almost all t. It is simpler and sufficient to set t∗ = t0, in which case, the value of a3 is given by (4.10), a3 It follows that the ball of H01(Ω) centered at 0 of radius ρ1 is absorbing in H01(Ω), when ρ12 =. + 2cε (c2 + 2c3cε)r + 2(2εr + 1) ρ0 2 + 2c1r + 4c3cεr , r > 0

Large-time behavior of the solutions

Conclusion