Convex integration yields nontrivial C^1 weak solutions of 2D elastodynamics from zero initial data under a weak null condition.
H\"{o}lder Continuous Solutions to the Three-dimensional Prandtl System
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abstract
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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2025 1verdicts
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The null condition in elastodynamics leads to non-uniqueness
Convex integration yields nontrivial C^1 weak solutions of 2D elastodynamics from zero initial data under a weak null condition.