Skip to content
DraconiticResearch
Search Sources API
206,690 studies31 sourcesUpdated 38 min ago
PreprintarXiv licencearXiv

Higher-order Sobolev stability and temporal decay estimate for the tropical climate model with small H1 data

  • Hyunjin In
  • Dong-ha Kim
  • Junha Kim
Open at sourcePDFDOICite

Abstract

We study the stability and temporal decay of solutions to the two-dimensional tropical climate model with Laplacian dissipation in both velocity equations and no thermal diffusion. For initial data in Hs (ℝ2) (s ≥ 1) with sufficiently small H1 norm, we establish a unique global solution satisfying uniform Hs bounds and time-integrated estimates for the velocity and temperature. The smallness is independent of s, and the higher Sobolev norms of the initial data need not be small. Furthermore, without additional spatial integrability or negative-order regularity of the initial data, we prove that the Ḣs (ℝ2) norms of the solutions are o(t− s / 2) as t → ∞. We also show that this decay rate is sharp: no additional decay factor tending to zero works for all such initial data.

Related

  1. On the Stability of Critical Points of the Hardy-Littlewood-Sobolev Inequality
    Kuan Liu, Qian Zhang, Wenming Zou
    Potential AnalysisPeer-reviewedLicence not statedFull text10 citedGeneral mathematicsOpenAlex
  2. On the Sobolev stability threshold for 3D Navier-Stokes equations with rotation near the Couette flow
    Wenting Huang, Ying Sun, Xiaojing Xu
    Calculus of Variations and Partial Differential EquationsPeer-reviewedLicence not statedFull text12 citedGeneral mathematicsOpenAlex
  3. Sharpness and Planar Stability of the Alexandrov-Bakelman-Pucci Estimate: a Convex Geometric Approach
    Antonio Porricelli
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. Sharp Quantitative Stability for the Affine p-Sobolev Inequality, Part II: The Case 1<p<2
    Song Fan, Gui-Dong Li, Jianjun Zhang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Stability under mixtures of transportation inequalities and restricted log-Sobolev inequalities
    Radosław Adamczak, Dominik Kutek, Michał Strzelecki
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{in2026higherorder,
  title = {{Higher-order Sobolev stability and temporal decay estimate for the tropical climate model with small $H^1$ data}},
  author = {Hyunjin In and Dong-ha Kim and Junha Kim},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.10989},
  eprint = {2611.10989},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.10989},
}
RIS
TY  - UNPB
TI  - Higher-order Sobolev stability and temporal decay estimate for the tropical climate model with small H^1 data
AU  - Hyunjin In
AU  - Dong-ha Kim
AU  - Junha Kim
PY  - 2026
DA  - 2026/11/07
PB  - arXiv
DO  - 10.48550/arxiv.2611.10989
UR  - https://arxiv.org/abs/2611.10989
AB  - We study the stability and temporal decay of solutions to the two-dimensional tropical climate model with Laplacian dissipation in both velocity equations and no thermal diffusion. For initial data in H^s (ℝ^2) (s ≥ 1) with sufficiently small H^1 norm, we establish a unique global solution satisfying uniform H^s bounds and time-integrated estimates for the velocity and temperature. The smallness is independent of s, and the higher Sobolev norms of the initial data need not be small. Furthermore, without additional spatial integrability or negative-order regularity of the initial data, we prove that the Ḣ^s (ℝ^2) norms of the solutions are o(t^− s / 2) as t → ∞. We also show that this decay rate is sharp: no additional decay factor tending to zero works for all such initial data.
ER  -