Global Classical Solutions for Non-Isentropic Navier-Stokes
Research Paper#Fluid Dynamics, Navier-Stokes Equations🔬 Research|Analyzed: Jan 3, 2026 08:41•
Published: Dec 31, 2025 11:38
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•ArXivAnalysis
This paper addresses a long-standing open problem in fluid dynamics: finding global classical solutions for the multi-dimensional compressible Navier-Stokes equations with arbitrary large initial data. It builds upon previous work on the shallow water equations and isentropic Navier-Stokes equations, extending the results to a class of non-isentropic compressible fluids. The key contribution is a new BD entropy inequality and novel density estimates, allowing for the construction of global classical solutions in spherically symmetric settings.
Key Takeaways
- •Proves the existence of global classical solutions for a class of non-isentropic compressible fluids.
- •Employs a new BD entropy inequality and novel density estimates.
- •Extends previous results on shallow water and isentropic Navier-Stokes equations.
- •Applies to spherically symmetric initial-boundary value problems in two and three dimensions.
- •Relaxes restrictions on dimension and adiabatic index compared to prior work.
Reference / Citation
View Original"The paper proves a new BD entropy inequality for a class of non-isentropic compressible fluids and shows the "viscous shallow water system with transport entropy" will admit global classical solutions for arbitrary large initial data to the spherically symmetric initial-boundary value problem in both two and three dimensions."