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

2023/07/13 by Song, Zihao
#35D05 #35Q31 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.06511

Abstract

We are concerned with the global solution of the compressible Euler-Korteweg equations in ℝ³. In the case of zero sound speed P'(ρ^∗)=0, it is found that the perturbation problem of irrotational fluids could be reformulated into a quasi-linear Schrodinger equation. Based on techniques of dispersive estimates and methods of normal form, we construct a class of global scattering solutions for 3D case.

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