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Global well-posedness of the stochastic electrokinetic flow with the mixed boundary conditions

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Veröffentlicht/Copyright: 23. Juli 2025
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 38 Heft 2

Abstract

We investigate the stochastic electrokinetic flow modelled by a stochastic Nernst–Planck–Navier–Stokes system with a blocking boundary condition for ionic species concentrations in a smooth bounded domain 𝒟. In both 2 ⁢ D and 3 ⁢ D cases, we establish the global existence of weak martingale solutions when the capacitance ς > 0 , and also establish the existence of a unique maximal strong pathwise solution when the capacitance ς = 0 . Moreover, by a probability estimate, we build the blow-up criterion. We finally show that the maximal pathwise solution is global in the 2 ⁢ D case without the restriction of smallness of initial data. In particular, the mixed boundary condition and the random effect bring essential difficulties in constructing approximate solutions and obtaining the a priori estimates which are totally different from the deterministic case. We develop the L 1 -energy conservation and the linearization techniques to overcome these difficulties.

Keywords: Stochastic Nernst–Planck–Navier–Stokes system; weak martingale solution; maximal pathwise solution; global pathwise solution; stochastic compactness; blow-up criterion; fixed point theorem
MSC 2020: 35Q35; 76D05; 35R60; 35A01

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 12401305

Award Identifier / Grant number: 12471208

Funding source: Natural Science Foundation of Jiangsu Province

Award Identifier / Grant number: BK20240721

Funding source: Natural Science Foundation of Chongqing Municipality

Award Identifier / Grant number: CSTB2023NSCQ-MSX0396

Funding statement: Zhaoyang Qiu is supported by the National Natural Science Foundation of China (Grant No. 12401305), the National Science Foundation for Colleges and Universities in Jiangsu Province (Grant No. 24KJB110011) and the National Science Foundation of Jiangsu Province (Grant No. BK20240721). Huaqiao Wang is supported by the National Natural Science Foundation of China (Grant No. 12471208), the Natural Science Foundation of Chongqing (Grant No. CSTB2023NSCQ-MSX0396).

Acknowledgements

We would like to thank the referee for the valuable suggestions and comments on the manuscript.

  1. Communicated by: Guozhen Lu

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Received: 2023-11-07
Revised: 2024-05-30
Published Online: 2025-07-23
Published in Print: 2026-01-01

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. A density version of Hua’s theorem
  3. Diagonals of solutions of the Yang–Baxter equation
  4. Log-correlation for shifted Dirichlet 𝐿-functions and Dedekind zeta functions of quadratic fields
  5. Subconvex bound for GL(3) × GL(2) L-functions: GL(3)-spectral aspect
  6. Continuity properties of multi-parameter pseudodifferential operators
  7. Sharp constants for fractional Hardy–Littlewood maximal operators on finite graphs
  8. Shifting the ordinates of zeros of the Riemann zeta function
  9. The sum of a prime power and an almost prime
  10. Unipotent mixing for general moduli
  11. The center of the Hecke algebra of a type
  12. Separability properties of extended admissible groups
  13. Small gaps between almost-twin primes
  14. Moments of primes in progressions to a large modulus
  15. Global well-posedness of the stochastic electrokinetic flow with the mixed boundary conditions
https://doi.org/10.1515/forum-2023-0401
Schlagwörter für diesen Artikel
Stochastic Nernst–Planck–Navier–Stokes system; weak martingale solution; maximal pathwise solution; global pathwise solution; stochastic compactness; blow-up criterion; fixed point theorem

Artikel in diesem Heft

  1. Frontmatter
  2. A density version of Hua’s theorem
  3. Diagonals of solutions of the Yang–Baxter equation
  4. Log-correlation for shifted Dirichlet 𝐿-functions and Dedekind zeta functions of quadratic fields
  5. Subconvex bound for GL(3) × GL(2) L-functions: GL(3)-spectral aspect
  6. Continuity properties of multi-parameter pseudodifferential operators
  7. Sharp constants for fractional Hardy–Littlewood maximal operators on finite graphs
  8. Shifting the ordinates of zeros of the Riemann zeta function
  9. The sum of a prime power and an almost prime
  10. Unipotent mixing for general moduli
  11. The center of the Hecke algebra of a type
  12. Separability properties of extended admissible groups
  13. Small gaps between almost-twin primes
  14. Moments of primes in progressions to a large modulus
  15. Global well-posedness of the stochastic electrokinetic flow with the mixed boundary conditions
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