On well-posedness of α-SQG equations in the half-plane

2023/05/07 by In‐Jee Jeong, Junha Kim, Jeong, In-Jee +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2305.04300

openalex publication_date 2023/05/07 · openalex created_date 2023/05/10 · openalex updated_date 2026/07/28

Abstract

We investigate the well-posedness of α-SQG equations in the half-plane, where α=0 and α=1 correspond to the 2D Euler and SQG equations respectively. For 0<α≤ 1/2, we prove local well-posedness in certain weighted anisotropic Hölder spaces. We also show that such a well-posedness result is sharp: for any 0<α≤ 1, we prove nonexistence of Hölder regular solutions (with the Hölder regularity depending on α) for initial data smooth up to the boundary.

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