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H\"{o}lder Continuous Solutions to the Three-dimensional Prandtl System

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arxiv 1804.04285 v1 pith:WIFSYFB5 submitted 2018-04-12 math.AP

Tianwen Luo , Zhouping Xin This is my paper · ORCID
classification math.AP
keywords continuouslderprandtlsolutionssystemadaptingconstructconvex
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Adapting the convex integration technique introduced by De Lellis and Sz{\'e}kelyhidi, we construct H\"{o}lder continuous weak solutions to the three dimensional Prandtl system and some other models with vertical viscosity.

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Cited by 3 Pith papers

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

  1. The null condition in elastodynamics leads to non-uniqueness

    math.AP 2025-02 conditional novelty 7.0 of 10

    Convex integration yields nontrivial C^1 weak solutions of 2D elastodynamics from zero initial data under a weak null condition.

  2. Non-uniqueness for the nonlinear dynamical Lam\'e system

    math.AP 2025-02 reject novelty 6.0 of 10

    Non-uniqueness of C^{1,alpha} weak solutions for the nonlinear dynamical Lame system is claimed via convex integration, but the constructed solutions fail the paper's H2 weak-solution regularity condition.

  3. Prandtl Equations and Related Boundary Layer Equations

    math.AP 2024-11 unverdicted novelty 5.0 of 10

    The book claims new well-posedness theorems for Prandtl and MHD boundary layer equations, but the provided text only shows the survey portion.

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