pith. sign in

arxiv: 2509.01268 · v2 · pith:4S5MD2ASnew · submitted 2025-09-01 · 🧮 math.AP

Global Existence, Hamiltonian Conservation and Vanishing Viscosity for the Surface Quasi-Geostrophic Equation

Luigi De Rosa , Micka\"el Latocca , Jaemin Park This is my paper
classification 🧮 math.AP
keywords frachamiltoniannormequationexistenceinitialquasi-geostrophicsolution
0
0 comments X
read the original abstract

For any initial datum $\theta_0\in L^{\frac{4}{3}}_x$ it is proved the existence of a global-in-time weak solution $\theta \in L^\infty_t L^{\frac43}_x$ to the surface quasi-geostrophic equation whose Hamiltonian, i.e. the $\dot{H}^{-\frac{1}{2}}_x$ norm, is constant in time. The solution is obtained as a vanishing viscosity limit. The main idea is to propagate in time the non-concentration of the $L^{\frac{4}{3}}_x$ norm of the initial data, from which the strong compactness in the Hamiltonian norm is deduced. Minimal Onsager supercritical conditions preventing anomalous dissipation are given.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Mixed Third-Order Flux Laws for Dual Cascade in the Stochastic SQG Equation

    math.AP 2026-06 unverdicted novelty 7.0

    Derives rigorous third-order flux laws for direct SPE and inverse Hamiltonian cascades in stochastic SQG and proves regularity obstructions to non-zero fluxes.

  2. Mixed Third-Order Flux Laws for Dual Cascade in the Stochastic SQG Equation

    math.AP 2026-06 unverdicted novelty 7.0

    Establishes rigorous third-order flux laws for direct SPE and inverse Hamiltonian cascades in stochastic SQG with Onsager obstructions under weak anomalous dissipation.

  3. Hamiltonian compactness and dissipation for the generalized SQG equation in the inviscid limit

    math.AP 2026-04 unverdicted novelty 7.0

    Strong compactness in the lowest norm making the nonlinearity well-defined prevents anomalous Hamiltonian dissipation for the generalized SQG equation in the inviscid limit, yielding global conservative weak solutions...

  4. Absence of local anomalous dissipation and local energy balance in 2D incompressible flows away from the boundary

    math.AP 2026-06 unverdicted novelty 6.0

    Local anomalous dissipation vanishes for 2D NS solutions bounded in L^{1+}_t L^∞_{x,loc} away from the boundary, yielding convergence to an Euler solution whose large-scale approximation satisfies local energy balance...