Kitchen faucet comes on strong but then tapers off

[Betty]

We've had an issue with our kitchen faucet as long as we've lived here: When you turn on the water in the kitchen sink it comes on strong but almost immediately the water stream dwindles to maybe half as much - sometimes more.

This is a double handle single spout faucet and it happens with both hot and cold water. You can sometimes get it to work a little longer by not turning the handle all the way on.

Does this sound like something that can be repaired or do we need a new sink? What would you call that? I can look up how to videos to fix things but I'm not sure what to refer to that as. (I love how to videos online to learn how to fix things.)