What question did this study set out to answer?

The aim is to establish higher-order commutator estimates for the pressure Hessian in three-dimensional incompressible fluid flows.

July 14, 20260 citationsOpen Access

On Calderon Zygmund Commutator Estimates for the Incompressible Pressure Hessian in Fractional Sobolev Spaces

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ESEfe SARICI

Key Points

The aim is to establish higher-order commutator estimates for the pressure Hessian in three-dimensional incompressible fluid flows.
Utilized a localized Littlewood-Paley decomposition
Employed the Calderón-Zygmund framework
Focused on fractional Sobolev spaces H^s(R^3) for s > 5/2.
Proved sharp bounds for the commutator [RiRj , u · ∇] in the specified spaces
Demonstrated intrinsic geometric control over localized oscillations of the pressure field
Avoided structural smallness assumptions on the velocity field.

Abstract

In this paper, we establish novel higher-order commutator estimates for the pressureHessian associated with three-dimensional incompressible fluid flows. By employing a localizedLittlewood-Paley decomposition and utilizing the classic Calder´on-Zygmund framework, weprove sharp bounds for the commutator RiRj, u · ∇ in fractional Sobolev spaces Hˢ (R3) fors > 5/2. These estimates provide an intrinsic geometric control over the localized oscillations ofthe pressure field without enforcing structural smallness assumptions on the velocity field.

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On Calderon Zygmund Commutator Estimates for the Incompressible Pressure Hessian in Fractional Sobolev Spaces

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