Forward self-similar solutions to the MHD equations: existence and pointwise estimates

Yifan Yang

Forward self-similar solutions to the MHD equations: existence and pointwise estimates

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arxiv 2404.02601 v3 pith:MK5XQDYJ submitted 2024-04-03 math.AP

Yifan Yang This is my paper · ORCID

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keywords forwardself-similarsolutionsequationspointwisespaceargumentblow-up

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abstract

In this paper, we study the forward self-similar solutions to the three-dimensional Magnetohydrodynamic equations (MHD equations) in the whole space. By employing the Leray-Schauder theorem and blow-up argument, we construct a global-time forward self-similar solutions, which is smooth in $\R^{3}\times(0,\infty)$. Furthermore, by investigating the regularity of the weak solutions to the corresponding Leray system in the weighted Sobolev space, we can derive the pointwise estimate for the forward self-similar solution.

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Weak and mild solutions to the MHD equations and the viscoelastic Navier-Stokes equations with damping in Wiener amalgam spaces
math.AP 2025-06 conditional novelty 4.0 of 10

Existence, spacetime bounds, eventual regularity and uniqueness are established for MHD and damped viscoelastic Navier-Stokes solutions in Wiener amalgam spaces, extending the Navier-Stokes theory.

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