Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
120 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
44 tokens/sec
o3 Pro
5 tokens/sec
GPT-4.1 Pro
3 tokens/sec
DeepSeek R1 via Azure Pro
55 tokens/sec
2000 character limit reached

Ergodicity for Ginzburg-Landau equation with complex-valued space-time white noise on two-dimensional torus (2408.11568v1)

Published 21 Aug 2024 in math.PR

Abstract: We investigate the ergodicity for the stochastic complex Ginzburg-Landau equation with a general non-linear term on the two-dimensional torus driven by a complex-valued space-time white noise. Due to the roughness of complex-valued space-time white noise, this equation is a singular stochastic partial differential equation and its solution is expected to be a distribution-valued stochastic process. For this reason, the non-linear term is ill-defined and needs to be renormalized. We first use the theory of complex multiple Wiener-Ito integral to renormalize this equation and then consider its global well-posedness. Further, we prove its ergodicity using an asymptotic coupling argument for a large dissipation coefficient.

Summary

We haven't generated a summary for this paper yet.

Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

We haven't generated follow-up questions for this paper yet.

X Twitter Logo Streamline Icon: https://streamlinehq.com