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

https://arxiv.org/abs/2311.07173

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

 

이 논문의 서론에서는 3D 비압축성 정상 상태의 Navier-Stokes 방정식에 대한 약해의 고유성을 연구합니다. 저자들은 특히 유체의 속도 $\vec{u}$에 대한 추가적인 정보를 Lebesgue 공간의 변동 지수 $L^{p(\cdot)}\left(\mathbb{R}^3\right)$를 이용하여 표현하고, 이를 통해 문제의 새로운 해결책을 제시합니다. 이들은 $L^{p(\cdot)}$ 공간이 기존의 $L^p$ 공간과는 다른 특성을 가진다고 지적하며, 이 공간을 활용하여 Liouville 형식의 고유성 결과를 도출하는 것이 이 논문의 주요 목적입니다. 또한, 이러한 접근 방식이 $\frac{9}{2} < p$인 경우에도 $\vec{u} \equiv 0$임을 증명하는 데 도움이 될 것으로 기대합니다.