platform is .net Core 2.1

the client is a Mvc client

at present, the login and logout functions are normal, and the authentication Cookie has been cleared after closing the browser. The problem encountered is to close the browser, and then open the browser to access the authentication page without entering the account number and password to log in. It is said that the client Cookie expires after closing the browser, and then open the browser to jump to the authentication page. You should log in again

is it because you did not log out correctly from the server? Do I need to log out from the server when I close the browser?