Traveling waves near shear flows for the inhomogeneous Euler equations with non-constant density
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912866622242816 |
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| author | Zhao, Qi Zhao, Weiren |
| author_facet | Zhao, Qi Zhao, Weiren |
| contents | We investigate the existence and nonexistence of traveling wave solutions near monotonic shear flows with non-constant background density for the two-dimensional inhomogeneous Euler equations in a finite channel. For any small $τ>0$, first, we construct nontrivial traveling waves with velocity and density in $H^{5/2-τ}$ and $H^{3/2-τ}$, respectively, showing that inviscid damping fails at these regularities. Second, when the distorted Rayleigh operator has no eigenvalues, we prove that such traveling wave solutions cannot exist in higher regularity spaces ($H^{5/2+τ}$ for velocity and $H^{3/2+τ}$ for density). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00824 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Traveling waves near shear flows for the inhomogeneous Euler equations with non-constant density Zhao, Qi Zhao, Weiren Analysis of PDEs We investigate the existence and nonexistence of traveling wave solutions near monotonic shear flows with non-constant background density for the two-dimensional inhomogeneous Euler equations in a finite channel. For any small $τ>0$, first, we construct nontrivial traveling waves with velocity and density in $H^{5/2-τ}$ and $H^{3/2-τ}$, respectively, showing that inviscid damping fails at these regularities. Second, when the distorted Rayleigh operator has no eigenvalues, we prove that such traveling wave solutions cannot exist in higher regularity spaces ($H^{5/2+τ}$ for velocity and $H^{3/2+τ}$ for density). |
| title | Traveling waves near shear flows for the inhomogeneous Euler equations with non-constant density |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.00824 |