The dynamical Φ₃⁴ model by an approximation of Laplacian

2023/03/31 by Reo Adachi, Adachi, Reo
Mathematics · Physics and Astronomy · #35R60 #60H17 #81S20 #81T08 #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2303.17772

openalex publication_date 2023/03/31 · openalex created_date 2023/04/06 · openalex updated_date 2026/07/28

Abstract

The dynamical Φ⁴₃ equation is a singular SPDE and has important applications in physics. In this paper, we consider the equation by approximating the Laplacian instead of the noise or the cubic term as in previous studies. By using a good transformation as in [JP21], we show that the approximating equation is locally well-posed and that its solution converges to the solution of the dynamical Φ⁴₃ equation. We expect to be able to show the global well-posedness and the existence of the invariant measure.

Related

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