Global Sobolev persistence for the fractional Boussinesq equations with\n zero diffusivity

2019/10/24 by Igor Kukavica, Weinan Wang, Kukavica, Igor +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1910.11307

openalex publication_date 2019/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We address the persistence of regularity for the 2D \α-fractional\nBoussinesq equations with positive viscosity and zero diffusivity in general\nSobolev spaces, i.e., for (u₀, \ρ₀) \∈ W^s,q( mathbb R²) \×\nW^s,q( mathbb R²), where s> 1 and q \∈ (2, \∞). We prove that the\nsolution (u(t), \ρ(t)) exists and belongs to W^s,q( mathbb R²) \×\nW^s,q( mathbb R²) for all positive time t for q>2, where\n\α\∈(1,2) is arbitrary.\n

Citations

• Global regularity for the 2D Boussinesq equations with partial viscosity terms

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