My mobile phone is N70. Is there a blacklist of short messages? What if someone keeps sending me harassing text messages?

Actually, there is no need for a blacklist. You can write down the number that sent you the text message, including the time and date of the text message, and then if it is mobile, just call 10086 to complain about harassment. They will take care of it for you. If Unicom is connected, call Unicom customer service, which can be completely solved!