On the well-posedness in Besov-Herz spaces for the inhomogeneous incompressible Euler equations

Lucas C. F. Ferreira; Daniel F. Machado

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arXiv · 2301.07765

On the well-posedness in Besov-Herz spaces for the inhomogeneous incompressible Euler equations

Lucas C. F. Ferreira·Daniel F. Machado

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Abstract

In this paper we study the inhomogeneous incompressible Euler equations in the whole space $\mathbb{R}^n$ with $n\geq3$. We obtain well-posedness and blow-up results in a new framework for inhomogeneous fluids, more precisely Besov-Herz spaces that are Besov spaces based on Herz ones, covering particularly critical cases of the regularity. Comparing with previous works on Besov spaces, our results provide a larger initial data class for a well-defined flow. For that, we need to obtain suitable linear estimates for some conservation-law models in our setting such as transport equations and the linearized inhomogeneous Euler system.

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BibTeX RIS

Lucas C. F. Ferreira, Daniel F. Machado. 2023-01-18. On the well-posedness in Besov-Herz spaces for the inhomogeneous incompressible Euler equations. https://arxiv.org/abs/2301.07765

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