Global existence of Euler-Korteweg equations with the non-monotone pressure

Fuente: arXiv
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Main Author: Song, Zihao
Format: Preprint
Published: 2023
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author Song, Zihao
author_facet Song, Zihao
contents We are concerned with the global solution of the compressible Euler-Korteweg equations in $\mathbb{R}^{3}$. In the case of zero sound speed $P'(ρ^{\ast})=0$, it is found that the perturbation problem of irrotational fluids could be reformulated into a quasi-linear Schr$\ddot{o}$dinger equation. Based on techniques of dispersive estimates and methods of normal form, we construct a class of global scattering solutions for 3D case.
format Preprint
id arxiv_https___arxiv_org_abs_2307_06511
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Global existence of Euler-Korteweg equations with the non-monotone pressure
Song, Zihao
Analysis of PDEs
76N10, 35D05, 35Q31
We are concerned with the global solution of the compressible Euler-Korteweg equations in $\mathbb{R}^{3}$. In the case of zero sound speed $P'(ρ^{\ast})=0$, it is found that the perturbation problem of irrotational fluids could be reformulated into a quasi-linear Schr$\ddot{o}$dinger equation. Based on techniques of dispersive estimates and methods of normal form, we construct a class of global scattering solutions for 3D case.
title Global existence of Euler-Korteweg equations with the non-monotone pressure
topic Analysis of PDEs
76N10, 35D05, 35Q31
url https://arxiv.org/abs/2307.06511