Results of Fractional Rough Burgers equation in H^s space and its application

2025/11/28 by Shuolin Zhang, Zhang, Shuolin, Zhaonan Luo +3
Engineering · Mathematics · #35Q35 #42B37 #60H15 #60H17 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2511.22900

openalex publication_date 2025/11/28 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the well-posedness of Fractional Rough Burgers equation driven by space-time noise in H^s(\mathbb T) space. For the higher dissipation γ∈((4)/(3),2], we establish local well-posedness. Global well-posedness is further obtained when γ is restricted to the interval ((5)/(3), 2]. For the lower dissipation γ∈((5)/(4),(4)/(3)], we use the regularity analysis derivation the para-controlled solution.

Citations

• The probabilistic scaling paradigm
• Random tensors, propagation of randomness, and nonlinear dispersive equations
• Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity
• Higher order expansions for the probabilistic local Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ³
• Paracontrolled Distributions and the 3-dimensional Stochastic Quantization Equation
• The Kato-Ponce Inequality
• Paracontrolled distributions and singular PDEs
• Solving the KPZ equation
• A New Integrable Equation with Peakon Solutions

Related

• Blow up and regularity for fractal Burgers equation
• Regularity of solutions for the critical N-dimensional Burgers' equation
• Global well-posedness and regularity of 3D Burgers equation with multiplicative noise
• Stochastic Burgers equation with fractional derivative driven by multiplicative noise
• Low regularity well-posedness of nonlocal dispersive perturbations of Burgers' equation