Asymptotic Stability of the Magnetohydrodynamic Flows with Temperature-Dependent Transport Coefficients
The objective of this paper is to analyze the asymptotic stability of global strong solutions to the boundary value problem of the compressible magnetohydrodynamic (MHD) equations for the ideal polytropic gas in which the viscosity <inline-formula><math xmlns="http://www.w3.org/1998/Ma...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/2/100 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | The objective of this paper is to analyze the asymptotic stability of global strong solutions to the boundary value problem of the compressible magnetohydrodynamic (MHD) equations for the ideal polytropic gas in which the viscosity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> and heat conductivity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>κ</mi></semantics></math></inline-formula> depend on temperature, i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>=</mo><msup><mi>θ</mi><mi>α</mi></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>κ</mi><mo>=</mo><msup><mi>θ</mi><mi>β</mi></msup></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>,</mo><mi>β</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>+</mo><mo>∞</mo><mo>)</mo></mrow></semantics></math></inline-formula>. Both the global-in-time existence and uniqueness of strong solutions are obtained under certain assumptions on the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and initial data. Moreover, based on accurate uniform-in-time estimates, we show that the global large solutions decay exponentially in time to the equilibrium states. Compared with the existing results, the initial data could be large if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> is small and the growth exponent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> can be arbitrarily large. |
|---|---|
| ISSN: | 2075-1680 |