L2−L∞ decay estimates and inviscid limits for Global smooth solutions to the compressible Navier-Stokes-Riesz system
Abstract
We study the Cauchy problem in ℝ3 for the repulsive compressible Navier-Stokes-Riesz system with Riesz exponent 0<s<1 and viscosity 0<ε≤1, where the Riesz interaction ∇(−Δ)−s(ρ−ρ̅) is a generalization of the Coulomb interaction for electrons. For small perturbations of a constant equilibrium, with the solenoidal component of the initial velocity of order 𝒪(ε), we prove the global existence and uniqueness of smooth solutions. We derive time-decay estimates in L2 norms and L∞ norms that capture both uniform-in-ε dispersive behavior and viscosity-dependent dissipation. We further establish a global-in-time inviscid limit to the irrotational global solution of the compressible Euler-Riesz system whose initial data consist of the same density and the curl-free component of the velocity, with an explicit convergence rate in Wk,p norms. The proof combines viscosity-adapted dispersive estimates, normal-form analysis and nonlinear energy estimates with control of both negative and positive Sobolev norms.
Related
- Global existence and decay estimates of solutions for the compressible Prandtl type equations in Sobolev spaces
- Boundary Layer Criterion for the Low Mach Number and Inviscid Limits in Compressible Fluid-Rigid Body Interaction
- A Necessary and Sufficient Condition for the Existence of Global Smooth Solutions to the One-Dimensional Inviscid Burgers-Vlasov System
- Global existence of solutions to the 2D compressible nematic liquid crystal flows with large initial data and vacuum
- Optimal L^2 Error Estimates for CSLDG Ideal Numerical Solutions in Time-Dependent Compressible Periodic Flows
BibTeX
@misc{swierczewskagwiazda2026decay,
title = {{$L^2-L^\infty$ decay estimates and inviscid limits for Global smooth solutions to the compressible Navier-Stokes-Riesz system}},
author = {Agnieszka Świerczewska-Gwiazda and Yuan Xu and Junhao Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.05562},
eprint = {2607.05562},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.05562},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - L^2−L^∞ decay estimates and inviscid limits for Global smooth solutions to the compressible Navier-Stokes-Riesz system
AU - Agnieszka Świerczewska-Gwiazda
AU - Yuan Xu
AU - Junhao Zhang
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2607.05562
UR - https://arxiv.org/abs/2607.05562
AB - We study the Cauchy problem in ℝ^3 for the repulsive compressible Navier-Stokes-Riesz system with Riesz exponent 0<s<1 and viscosity 0<ε≤1, where the Riesz interaction ∇(−Δ)^−s(ρ−ρ̅) is a generalization of the Coulomb interaction for electrons. For small perturbations of a constant equilibrium, with the solenoidal component of the initial velocity of order 𝒪(ε), we prove the global existence and uniqueness of smooth solutions. We derive time-decay estimates in L^2 norms and L^∞ norms that capture both uniform-in-ε dispersive behavior and viscosity-dependent dissipation. We further establish a global-in-time inviscid limit to the irrotational global solution of the compressible Euler-Riesz system whose initial data consist of the same density and the curl-free component of the velocity, with an explicit convergence rate in W^k,p norms. The proof combines viscosity-adapted dispersive estimates, normal-form analysis and nonlinear energy estimates with control of both negative and positive Sobolev norms.
ER -