Research Paper#Stochastic Partial Differential Equations, Wave Equations, Noise🔬 ResearchAnalyzed: Jan 3, 2026 19:00
Stochastic Wave Equations with Transport Noise
Published:Dec 29, 2025 08:56
•1 min read
•ArXiv
Analysis
This paper investigates the impact of transport noise on nonlinear wave equations. It explores how different types of noise (acting on displacement or velocity) affect the equation's structure and long-term behavior. The key finding is that the noise can induce dissipation, leading to different limiting equations, including a Westervelt-type acoustic model. This is significant because it provides a stochastic perspective on deriving dissipative wave equations, which are important in various physical applications.
Key Takeaways
- •The paper studies nonlinear wave equations perturbed by transport noise.
- •Different types of noise (displacement vs. velocity) lead to different behaviors.
- •Noise acting on velocity can generate an effective dissipative term.
- •The study provides a stochastic derivation of a Westervelt-type acoustic model.
Reference
“When the noise acts on the velocity, the rescaled dynamics produce an additional Laplacian damping term, leading to a stochastic derivation of a Westervelt-type acoustic model.”