Global Existence and Nonlinear Stability of Finite-Energy Solutions of the Compressible Euler-Riesz Equations with Large Initial Data of Spherical Symmetry Article Swipe
José A. Carrillo
,
S.W. Charles
,
Gui‐Qiang Chen
,
Difan Yuan
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2502.13094
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2502.13094
The compressible Euler-Riesz equations are fundamental with wide applications in astrophysics, plasma physics, and mathematical biology. In this paper, we are concerned with the global existence and nonlinear stability of finite-energy solutions of the multidimensional Euler-Riesz equations with large initial data of spherical symmetry. We consider both attractive and repulsive interactions for a wide range of Riesz and logarithmic potentials for dimensions larger than or equal to two. This is achieved by the inviscid limit of the solutions of the corresponding Cauchy problem for the Navier-Stokes-Riesz equations. The strong convergence of the vanishing viscosity solutions is achieved through delicate uniform estimates in $L^p$. It is observed that, even if the attractive potential is super-Coulomb, no concentration is formed near the origin in the inviscid limit. Moreover, we prove that the nonlinear stability of global finite-energy solutions for the Euler-Riesz equations is unconditional under a spherically symmetric perturbation around the steady solutions. Unlike the Coulomb case where the potential can be represented locally, the singularity and regularity of the nonlocal radial Riesz potential near the origin require careful analysis, which is a crucial step. Finally, unlike the Coulomb case, a Grönwall type estimate is required to overcome the difficulty of the appearance of boundary terms in the sub-Coulomb case and the singularity of the super-Coulomb potential. Furthermore, we prove the nonlinear stability of global finite-energy solutions for the compressible Euler-Riesz equations around steady states by employing concentration compactness arguments. Steady states properties are obtained by variational arguments connecting to recent advances in aggregation-diffusion equations.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2502.13094
- https://arxiv.org/pdf/2502.13094
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4407760038
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https://openalex.org/W4407760038Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2502.13094Digital Object Identifier
- Title
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Global Existence and Nonlinear Stability of Finite-Energy Solutions of the Compressible Euler-Riesz Equations with Large Initial Data of Spherical SymmetryWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
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2025Year of publication
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2025-02-18Full publication date if available
- Authors
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José A. Carrillo, S.W. Charles, Gui‐Qiang Chen, Difan YuanList of authors in order
- Landing page
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https://arxiv.org/abs/2502.13094Publisher landing page
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https://arxiv.org/pdf/2502.13094Direct link to full text PDF
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2502.13094Direct OA link when available
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Euler equations, Nonlinear system, Stability (learning theory), Compressibility, Euler's formula, Symmetry (geometry), Mathematics, Mathematical analysis, Physics, Mathematical physics, Mechanics, Geometry, Quantum mechanics, Computer science, Machine learningTop concepts (fields/topics) attached by OpenAlex
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| abstract_inverted_index.equations | 3, 36, 139, 229 |
| abstract_inverted_index.estimates | 100 |
| abstract_inverted_index.existence | 25 |
| abstract_inverted_index.nonlinear | 27, 130, 219 |
| abstract_inverted_index.potential | 111, 157, 171 |
| abstract_inverted_index.repulsive | 49 |
| abstract_inverted_index.solutions | 31, 77, 94, 135, 224 |
| abstract_inverted_index.spherical | 42 |
| abstract_inverted_index.stability | 28, 131, 220 |
| abstract_inverted_index.symmetric | 145 |
| abstract_inverted_index.symmetry. | 43 |
| abstract_inverted_index.vanishing | 92 |
| abstract_inverted_index.viscosity | 93 |
| abstract_inverted_index.appearance | 200 |
| abstract_inverted_index.arguments. | 237 |
| abstract_inverted_index.attractive | 47, 110 |
| abstract_inverted_index.connecting | 246 |
| abstract_inverted_index.difficulty | 197 |
| abstract_inverted_index.dimensions | 61 |
| abstract_inverted_index.equations. | 86, 252 |
| abstract_inverted_index.potential. | 214 |
| abstract_inverted_index.potentials | 59 |
| abstract_inverted_index.properties | 240 |
| abstract_inverted_index.regularity | 165 |
| abstract_inverted_index.solutions. | 150 |
| abstract_inverted_index.Euler-Riesz | 2, 35, 138, 228 |
| abstract_inverted_index.compactness | 236 |
| abstract_inverted_index.convergence | 89 |
| abstract_inverted_index.fundamental | 5 |
| abstract_inverted_index.logarithmic | 58 |
| abstract_inverted_index.represented | 160 |
| abstract_inverted_index.singularity | 163, 210 |
| abstract_inverted_index.spherically | 144 |
| abstract_inverted_index.sub-Coulomb | 206 |
| abstract_inverted_index.variational | 244 |
| abstract_inverted_index.Furthermore, | 215 |
| abstract_inverted_index.applications | 8 |
| abstract_inverted_index.compressible | 1, 227 |
| abstract_inverted_index.interactions | 50 |
| abstract_inverted_index.mathematical | 14 |
| abstract_inverted_index.perturbation | 146 |
| abstract_inverted_index.astrophysics, | 10 |
| abstract_inverted_index.concentration | 115, 235 |
| abstract_inverted_index.corresponding | 80 |
| abstract_inverted_index.finite-energy | 30, 134, 223 |
| abstract_inverted_index.super-Coulomb | 213 |
| abstract_inverted_index.unconditional | 141 |
| abstract_inverted_index.super-Coulomb, | 113 |
| abstract_inverted_index.multidimensional | 34 |
| abstract_inverted_index.Navier-Stokes-Riesz | 85 |
| abstract_inverted_index.aggregation-diffusion | 251 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile |