Global Well-Posedness of Inhomogeneous Navier–Stokes Equations with Bounded Density
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Key Points
The study confirms the uniqueness of weak solutions for 2D inhomogeneous Navier–Stokes equations under bounded density conditions.
It extends earlier results for 3D incompressible Navier–Stokes equations, establishing global well-posedness for bounded density and small initial velocities.
Key methodological challenges arise from insufficient estimates regarding the gradient of velocity, affecting solution uniqueness.
These findings have significant implications for understanding stability within fluid dynamics under specific conditions.
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Implication
Analysis confirms uniqueness of weak solutions to 2D inhomogeneous Navier–Stokes equations, indicating stability for bounded conditions.