Geodesic
The pressureless damped Euler–Riesz equations
Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 3, pp. 593-630

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In this paper, we analyze the pressureless damped Euler–Riesz equations posed in either ℝ d or 𝕋 d . We construct the global-in-time existence and uniqueness of classical solutions for the system around a constant background state.We also establish large-time behaviors of classical solutions showing the solutions towards the equilibrium as time goes to infinity. For the whole space case, we first show an algebraic decay rate of solutions under additional assumptions on the initial data compared to the existence theory. We then refine the argument to have an exponential decay rate of convergence even in the whole space. In the case of the periodic domain, without any further regularity assumptions on the initial data, we provide the exponential convergence of solutions.

Accepté le :
Publié le :
DOI : 10.4171/aihpc/48
Classification : 35A09, 35B40
Keywords: Pressureless damped Euler–Riesz system, global well-posedness, large-time behavior, fractional negative-order Sobolev spaces, interpolation inequalities 
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     author = {Choi, Young-Pil and Jung, Jinwook},
     title = {The pressureless damped {Euler{\textendash}Riesz} equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {593--630},
     volume = {40},
     number = {3},
     year = {2023},
     doi = {10.4171/aihpc/48},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/48/}
}
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Choi, Young-Pil; Jung, Jinwook. The pressureless damped Euler–Riesz equations. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 3, pp. 593-630. doi: 10.4171/aihpc/48

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