I'm currently working on a small open source project called Automation.SQL. It is a formalization of my work first explored in this blog post about LocalDb. Justin Rusbatch and we hope to have it out on Nuget shortly (no pressure :P), but first I had to write a few tests around both current versions of LocalDb : v11.0 and v12.0. The first, powered by SQL Server Express 2012, worked like a charm, but the version 12.0 version failed to work on my machine. I did have SQL Express 2014 installed along with LocalDb, but I didn't have an instance. Trying to connect to it via SQL Server management studio (SSMS) ended in failure. Running the following command(s) in a command prompt fixed that.
LocalDB SQL EXPRESS 2014
"C:\Program Files\Microsoft SQL Server\120\Tools\Binn\SqlLocalDB.exe" create "v12.0" 12.0 -s
LocalDB SQL Express 2012
"C:\Program Files\Microsoft SQL Server\110\Tools\Binn\SqlLocalDB.exe" create "v11.0" 11.0 -s
Verify that the command worked by using SSMS to connect to the instance.
Hope this helps others looking to use the newer SQL Express 2014 engine with LocalDB.