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August 26, 2025Documenta Mathematica0 citationsOpen Access

Liouville-type theorems for stationary Navier–Stokes equations with Lebesgue spaces of variable exponent

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DCDiego ChamorroGVGastón Vergara-Hermosilla

Key Points

  • Weak solutions exhibit uniqueness under specific conditions on velocity fields, contributing to the understanding of fluid dynamics.
  • This work establishes connections to traditional spaces like morrey and bmo^-1, emphasizing the role of variable exponent lebesgue spaces.
  • The approach involves analyzing stationary 3D navier-stokes equations with a flexible framework for variable exponents.
  • Findings suggest that variable exponent spaces may broaden the scope of solutions for complex fluid behavior.

Abstract

In this article we study some Liouville-type theorems for the stationary 3D Navier–Stokes equations. These results are related to the uniqueness of weak solutions for this system under some additional information over the velocity field, which is usually stated in the literature in terms of Lebesgue, Morrey or BMO^-1 spaces. Here we will consider Lebesgue spaces of variable exponent which will provide us with some interesting flexibility.

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Cite This Study

Chamorro et al. (2025) studied this question.

synapsesocial.com/papers/68af63e3ad7bf08b1eae42b5https://doi.org/10.4171/dm/1018
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