Are registers stack, per core or per application based?

Question

I am doing a study on I found on youtube called OpenSecurityTraining: Introductory Intel x86. From what I understand there are registers like EAX, ECD, EDX, ect... and each have a purpose and hold/move information in memory.

Are these registers per stack/application? Meaning, each application will have it's own EAX, EDX, ect... that it uses to hold or move data in and out of memory?