SWhat changed
Kovalevskaya proved convergence of the recursively determined formal power series for analytic PDE Cauchy problems in the paper's normal, noncharacteristic forms. A coefficientwise majorant argument establishes the first-order system result; higher-order algebraic equations and specified coupled systems are reduced to this setting after selecting a simple root for the leading normal derivatives. Analytic initial data then determine a unique local analytic solution on that branch. She also exhibited heat-equation data whose formal time series has zero convergence radius, showing why solving for a lower-order time derivative alone is insufficient.
Scientific scope
Kovalevskaya proved convergence of the recursively determined formal power series for analytic PDE Cauchy problems in the paper's normal, noncharacteristic forms. A coefficientwise majorant argument establishes the first-order system result; higher-order algebraic equations and specified coupled systems are reduced to this setting after selecting a simple root for the leading normal derivatives. Analytic initial data then determine a unique local analytic solution on that branch. She also exhibited heat-equation data whose formal time series has zero convergence radius, showing why solving for a lower-order time derivative alone is insufficient. Local analytic existence and uniqueness for the stated nondegenerate normal-derivative conditions, not global solvability, stability in smooth norms or arbitrary C∞data. An algebraic leading equation may have multiple simple branches; uniqueness is after fixing the branch. Characteristic or singular leading-derivative roots are not automatically covered. The heat example concerns a joint analytic solution at the initial surface, not nonexistence of every one-sided smooth heat evolution. The paper credits Weierstrass's ODE framework and other predecessors; no exclusive first-priority claim for the whole later Cauchy–Kovalevskaya lineage is awarded.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. Local analytic existence and uniqueness for the stated nondegenerate normal-derivative conditions, not global solvability, stability in smooth norms or arbitrary C∞data. An algebraic leading equation may have multiple simple branches; uniqueness is after fixing the branch. Characteristic or singular leading-derivative roots are not automatically covered. The heat example concerns a joint analytic solution at the initial surface, not nonexistence of every one-sided smooth heat evolution. The paper credits Weierstrass's ODE framework and other predecessors; no exclusive first-priority claim for the whole later Cauchy–Kovalevskaya lineage is awarded.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.3. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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