In this article, we are going to explain about very common issue - local indexes issue
Few days back, I was also facing same issue that while trying to rebuild one of index from control panel.
There were no index listed on Indexing manager.
As I have attached screenshot
After looking at configs and running services.
Found that core name are not correct (as compare to search engine).
Since we are using solr, so we looked configs as
App_Config/Sitecore/ContentSearch/
~/Sitecore.ContentSearch.Solr.Index.Master.config
~/Sitecore.ContentSearch.Solr.Index.Web.config
~/Sitecore.ContentSearch.Solr.Index.Core.config
and compared core with Solr admin portal (my instance solr url is : https://localhost:8983)
and correcting corename into configs, indexes started listing.
Hope this will help.