Is the "case" in the recognition of well-known trademarks an ordinary case of trademark infringement?

Not really.
Some people think that the trademark is a large number of others counterfeit is the best reason to start the well-known trademark recognition, but in fact, such a case can not start the well-known trademark recognition process. According to the law, this infringement is an infringement of the exclusive right to use a registered trademark, and is not applicable to the recognition of well-known trademarks. Therefore, the "case" referred to in the recognition of well-known trademarks is a special trademark infringement case, not a case of infringement of the exclusive right to use a registered trademark in the general sense.