{"id":"https://openalex.org/keywords/weak-solutions","display_name":"weak solutions","description":"Solutions to differential equations that satisfy the equations in an integral or distributional sense, even when they lack classical differentiability.","display_name_alternatives":["weak solution","generalized solutions"],"ids":{"openalex":"https://openalex.org/keywords/weak-solutions","wikidata":"https://www.wikidata.org/wiki/Q7977966"},"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.2829,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.2829,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.1879,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.0834,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"works_count":24978,"cited_by_count":312382,"works_api_url":"https://api.openalex.org/works?filter=keywords.id:keywords/weak-solutions","updated_date":"2026-10-24T04:06:44","created_date":"2026-09-30T00:00:00"}