Existence and uniqueness in critical spaces for the magnetohydrodynamical system in $\mathbb{R}^n$

Clément Denis

Existence and uniqueness in critical spaces for the magnetohydrodynamical system in $\mathbb{R}^n$

Analysis of PDEs 2022-05-12 v1

Authors: Clément Denis

Abstract

We give a description of a magnetohydrodynamical system in $n$ dimension using the exterior derivative. We then prove existence of global solutions for small initial data and local existence for arbitrary large data in two classes of critical spaces -- $L^q_tL^p_x$ and $\mathcal{C}_tL^p_x$ , as well as uniqueness for solutions in $\mathcal{C}_tL^p_x$ .

Keywords

magnetohydrodynamical system exterior derivative critical spaces global solutions local existence uniqueness

Cite

@article{arxiv.2205.04071,
  title  = {Existence and uniqueness in critical spaces for the magnetohydrodynamical system in $\mathbb{R}^n$},
  author = {Clément Denis},
  journal= {arXiv preprint arXiv:2205.04071},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:2103.03555 by other authors

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