The pressureless damped Euler–Riesz equations

  • Young-Pil Choi

    Yonsei University, Seoul, South Korea
  • Jinwook Jung

    Jeonbuk National University, Jeonju, South Korea
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In this paper, we analyze the pressureless damped Euler–Riesz equations posed in either Rd\mathbb{R}^d or Td\mathbb{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.

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Young-Pil Choi, Jinwook Jung, The pressureless damped Euler–Riesz equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 40 (2023), no. 3, pp. 593–630

DOI 10.4171/AIHPC/48