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

Three-dimensional magnetohydrodynamics system forced by space-time white noise (1910.04820v3)

Published 10 Oct 2019 in math.AP

Abstract: We consider the three-dimensional magnetohydrodynamics system forced by noise that is white in both time and space. Its complexity due to four non-linear terms makes its analysis very intricate. Nevertheless, taking advantage of its structure and adapting the theory of paracontrolled distributions from \cite{GIP15}, we prove its local well-posedness. A first challenge is to find an appropriate paracontrolled ansatz which must consist of both the velocity and the magnetic fields. Second challenge is that for some non-linear terms, renormalizations cannot be achieved individually; we overcome this obstacle by strategically coupling certain terms together rather than separately. Our proof is also inspired by the work of \cite{ZZ15}.

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.

Authors (1)