%0 Journal Article
%T Global Well-Posedness and Large-Time Behavior to the 3D Two-Fluid Model with Degenerate Viscosities
%A Hongxia Ji
%A Wenjing Song
%J Journal of Applied Mathematics and Physics
%P 230-255
%@ 2327-4379
%D 2025
%I Scientific Research Publishing
%R 10.4236/jamp.2025.131010
%X In the paper, we study a compressible two-fluid model in <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <msup>
   <mi>&#x211D;</mi>
   <mn>3</mn>
  </msup>
  </mrow>
</math>

, where <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <msup>
   <mi>&#x03B3;</mi>
   <mo>&#x00B1;</mo>
  </msup>
  <mo>&#x003E;</mo><mn>1</mn></mrow>
</math>

. The pressure of the two fluids is equal. Different from previous research, we consider that viscosity coefficient both <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>&#x03BC;</mi>
</math>

 and <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>&#x03BB;</mi>
</math>

 are functions of density. The global well-posedness of the three-dimensional compressible two-phase flow model is an open problem due to its dissipative, nonlinear structure. In the paper, setting <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <msup>
   <mi>m</mi>
   <mo>&#x00B1;</mo>
  </msup>
  <mo>=</mo><msup>
   <mi>M</mi>
   <mo>&#x00B1;</mo>
  </msup>
  </mrow>
</math>

 and <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>Z</mi><mo>=</mo><mi>P</mi><mo>&#x2212;</mo><mover accent='true'>
   <mi>P</mi>
   <mo>&#x00AF;</mo>
  </mover>
  </mrow>
</math>

, by exploiting the dissipation structure, we obtain energy estimates for <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mrow><mo>(</mo>
   <mrow>
    <mi>Z</mi><mn>,</mn><mi>w</mi><mn>,</mn><mi>n</mi></mrow>
  <mo>)</mo></mrow></mrow>
</math>

 and its derivatives, then we obtain the time decay rates for <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mrow><mo>(</mo>
   <mrow>
    <mi>Z</mi><mn>,</mn><mi>w</mi><mn>,</mn><mi>n</mi></mrow>
  <mo>)</mo></mrow></mrow>
</math>

. So we derive global well-posedness and large time behavior to the three dimensional compressible two-fluid model.
%K Two-Fluid Model
%K Degenerate Viscosities
%K Large-Time Behavior
%K Global Well-Posedness
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=140077