2024/12/30 by Young-Pil Choi, Choi, Young-Pil, Jinwook Jung +3
Mathematics · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2412.20705
This paper investigates the global dynamics of the Euler--Riesz system in three dimensions, focusing on the well-posedness and large-time behavior of solutions near equilibrium. The system generalizes classical interactions by incorporating the Riesz interactions ∇ (-Δ)-σ/2(ρ- 1). We show that the system admits a global smooth solution for small irrotational initial perturbations. Specifically, we establish that if the initial data is sufficiently small, the solution remains regular globally in time and decays over time at a rate dependent on σ.