Connecting to SQL Server Express in silverlight 4 appl, the db doesn't shows up in Management Studio Express

Question

I'm using SQL Server Express named instance and LinqToSql in my Silverlight 4 application. The database located in the web application App_Data folder. I attached the db via VS2010.

The connection string generated by the program automatically, after double clicked on the db file.

When I load the solution, I get an error:

"The connection property in the Web.config file is missing or incorrect, the connection string from the .dbml file has been used instead"

The program works, but the db doesn't show up in Management Studio Express.

If I delete the connection from within VS2010, and Try to attach to db via Management Studio Express, on writes, that the database with the same name already exists.

Why the database connected via VS2010 doesn't show up in Management Studio Express?

What is the error in the automatically generated connection string, that refers to the database file directory:

<connectionStrings>
    <add name="FitnessTrackerPlusConnectionString" connectionString="Data Source=.\SQLEXPRESS;AttachDbFilename=|DataDirectory|\FitnessTrackerPlus.mdf;Integrated Security=True;User Instance=True"
        providerName="System.Data.SqlClient" />
</connectionStrings>

Thanks advance

Gabor