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<p>In this paper, we investigate the primitive three-dimensional dynamic equations for moist atmosphere with only horizontal dissipation. Especially, we introduce the phase transformation of water vapor, which are considered as some nonlinear functions related to temperature and pressure. For any <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>1</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$H^{1}$</EquationSource> </InlineEquation> initial data, the local well-posedness of strong solution can be established by decomposing velocity field into barotropic velocity field and baroclinic velocity field, as well as energy estimates method. Furthermore, applying logarithmic type Sobolev inequality, we can obtain the estimates of state functions in global time. Then the well-posedness of global strong solution can be proved.</p>

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Global Existence of the \(H^{1}\) Strong Solution to a Climate Dynamics Model with Horizontal Dissipation and Phase Transformation of Water Vapor

  • 期刊论文

  • 发表日期：

    2025年11月11日

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  • Ruxu Lian,
  • Yue Hu,
  • JieQiong Ma

摘要

In this paper, we investigate the primitive three-dimensional dynamic equations for moist atmosphere with only horizontal dissipation. Especially, we introduce the phase transformation of water vapor, which are considered as some nonlinear functions related to temperature and pressure. For any H 1 $H^{1}$ initial data, the local well-posedness of strong solution can be established by decomposing velocity field into barotropic velocity field and baroclinic velocity field, as well as energy estimates method. Furthermore, applying logarithmic type Sobolev inequality, we can obtain the estimates of state functions in global time. Then the well-posedness of global strong solution can be proved.