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Global large strong solutions to the compressible Navier-Stokes equations with density-dependent viscosities, case I: isentropic flows

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arxiv 2408.04305 v1 pith:EVYF6XIW submitted 2024-08-08 math.AP

Xiangdi Huang , Jiaxu Li , Rong Zhang This is my paper · ORCID
classification math.AP
keywords compressibledatadensity-dependentequationsglobalinitiallargenavier-stokes
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In this paper, we consider the Cauchy problem for the three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering the system as an elliptic-dominated structure and defining suitable energy functionals, after the elaborate index analysis, we establish the global existence of strong solutions as long as the initial data is large enough. This is a big contrast to the classical results where the initial data is a small perturbation of some resting states.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Global existence and optimal time-decay rates of the compressible Navier-Stokes equations with density-dependent viscosities

    math.AP 2025-07 reject novelty 6.0 of 10

    A proof is proposed that small L1∩L2 initial data yields global classical solutions and optimal time-decay rates when the viscosity exponent α is within δ of 1.

  2. Global strong solution of the 3D compressible liquid crystal flows with density-dependent viscosity and large velocity

    math.AP 2025-07 conditional novelty 6.0 of 10

    For 3D compressible liquid crystal flows with density-dependent viscosity, global strong solutions exist for large initial density and small director gradient, with no smallness condition on velocity.

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