NOT NULL として定義された MySQL カラムにゼロまたは空の文字列を挿入するにはどうすればよいですか?

mysql> Select 0 IS NULL, 0 IS NOT NULL;
+-----------+---------------+
| 0 IS NULL | 0 IS NOT NULL |
+-----------+---------------+
|         0 |             1 |
+-----------+---------------+
1 row in set (0.00 sec)

mysql> Select '' IS NULL, '' IS NOT NULL;
+------------+----------------+
| '' IS NULL | '' IS NOT NULL |
+------------+----------------+
|          0 |              1 |
+------------+----------------+
1 row in set (0.00 sec)

mysql> create table test(id int NOT NULL, Name Varchar(10));
Query OK, 0 rows affected (0.19 sec)

mysql> Insert into test6(id, name) values('1', 'Gaurav'),('0','Rahul'),('','Aarav');
Query OK, 3 rows affected, 1 warning (0.08 sec)
Records: 3 Duplicates: 0 Warnings: 1

Warning (Code 1366): Incorrect integer value: '' for column 'id' at row 3

mysql> Select * from test;
+----+--------+
| id | Name |
+----+--------+
|  1 | Gaurav |
|  0 | Rahul  |
|  0 | Aarav  |
+----+--------+
3 rows in set (0.00 sec)