mysql -u root できない

$ mysql -u root
すると以下のメッセージが出てしまいます。

ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO)

また、 $ mysqld すると以下のログが大量に流れてきます。

2016-04-22 21:29:28 0 [Warning] TIMESTAMP with implicit DEFAULT value is deprecated. Please use --explicit_defaults_for_timestamp server option (see documentation for more details).
2016-04-22 21:29:28 0 [Note] mysqld (mysqld 5.6.27) starting as process 42562 ...
2016-04-22 21:29:28 42562 [Warning] Setting lower_case_table_names=2 because file system for /usr/local/var/mysql/ is case insensitive
2016-04-22 21:29:28 42562 [Note] Plugin 'FEDERATED' is disabled.
2016-04-22 21:29:28 42562 [Note] InnoDB: Using atomics to ref count buffer pool pages
2016-04-22 21:29:28 42562 [Note] InnoDB: The InnoDB memory heap is disabled
2016-04-22 21:29:28 42562 [Note] InnoDB: Mutexes and rw_locks use GCC atomic builtins
2016-04-22 21:29:28 42562 [Note] InnoDB: Memory barrier is not used
2016-04-22 21:29:28 42562 [Note] InnoDB: Compressed tables use zlib 1.2.3
2016-04-22 21:29:28 42562 [Note] InnoDB: Using CPU crc32 instructions
2016-04-22 21:29:28 42562 [Note] InnoDB: Initializing buffer pool, size = 128.0M
2016-04-22 21:29:28 42562 [Note] InnoDB: Completed initialization of buffer pool
2016-04-22 21:29:28 42562 [ERROR] InnoDB: Unable to lock ./ibdata1, error: 35
2016-04-22 21:29:28 42562 [Note] InnoDB: Check that you do not already have another mysqld process using the same InnoDB data or log files.
2016-04-22 21:29:28 42562 [Note] InnoDB: Retrying to lock the first data file
2016-04-22 21:29:29 42562 [ERROR] InnoDB: Unable to lock ./ibdata1, error: 35
2016-04-22 21:29:29 42562 [Note] InnoDB: Check that you do not already have another mysqld process using the same InnoDB data or log files.
2016-04-22 21:29:30 42562 [ERROR] InnoDB: Unable to lock ./ibdata1, error: 35
2016-04-22 21:29:30 42562 [Note] InnoDB: Check that you do not already have another mysqld process using the same InnoDB data or log files.
2016-04-22 21:29:31 42562 [ERROR] InnoDB: Unable to lock ./ibdata1, error: 35
2016-04-22 21:29:31 42562 [Note] InnoDB: Check that you do not already have another mysqld process using the same InnoDB data or log files.
2016-04-22 21:29:32 42562 [ERROR] InnoDB: Unable to lock ./ibdata1, error: 35
2016-04-22 21:29:32 42562 [Note] InnoDB: Check that you do not already have another mysqld process using the same InnoDB data or log files.
2016-04-22 21:29:33 42562 [ERROR] InnoDB: Unable to lock ./ibdata1, error: 35
2016-04-22 21:29:33 42562 [Note] InnoDB: Check that you do not already have another mysqld process using the same InnoDB data or log files.

ちなみにMysqlはbrewでインストールしました。

よろしくお願いします。