Could you elaborate more your question? Are you asking for PDE types and their mathematical classification (via eigenvalues analysis) governing different flow problems?
Yes. I am interested in different PDEs, their solutions and main characteristics in a comparative form. Could you please help me by providing some useful materials or books?
I remember a synoptic table in the Hirsch book https://books.google.it/books?hl=it&lr=&id=bsrkrw5MdtUC&oi=fnd&pg=PP1&dq=charles+hirsch+numerical+computation+of+internal+and+external+flows+pdf&ots=a5vP2jUlCc&sig=G0VYKDIXJcSMWyfR8NGx9d_usos#v=onepage&q=charles%20hirsch%20numerical%20computation%20of%20internal%20and%20external%20flows%20pdf&f=false