If you want to use UNIX sockets with the Mysql JDBC Connector/J you need to provide a socketFactory.
jdbc:mysql:///?user=test&password=test&socketFactory=<classname>&<socket>=/tmp/mysql.sock
So this will vary with the implementation you use. By default, Mysql does not ship with any implementation for that, just provides an example for such a factory in it’s source-code.
There is an existing UNIX socket Java library named junixsocket which also has such a socketFactory class implementation. An example is outlined in Connecting to a MySQL database via Unix Domain Sockets which is part of their documentation.
You can find more Java UNIX socket library alternatives in related Q&A material: