There is ample evidence that who "we" are, in terms of specific thoughts, interests, memories, emotions, etc., is directly attributable to our physical brain & body.
We see some of this first-hand. For those of us who live deep into old age, many will experience changes to our physical bodies that fundamentally alter who we are. Some unlucky few will experience it earlier: traumatic brain injury, Alzheimer's, Lewy Body Dementia, to name a few.
Other aspects of it are apparent through the study of our brains. Researchers have observed, for instance, that "decisions" are made prior to conscious awareness.
So, to your question:
Do you believe you will exist in some fashion after you die?
I think the answer is plainly no. If by "you" you're referring to person-hood as described above, then it seems clear that as the body decays, any possibility of preservation of that identity is lost. When this body dies, so will its hopes and dreams. If I exist in any capacity after physical death, that being will not remember my life or love my family.
I suspect this same phenomenon occurs almost constantly at a much more gradual pace. I often think about how, as each day passes, a part of me, the version who was alive that day, ceases to exist. I have the perception of continuity because I have memories, and my behavior remains relatively constant by the day, but we actually can never be sure that we actually existed prior to the present moment.
That said, I have yet to hear any scientific or other reasoned explanation for consciousness (i.e. the phenomenon whereby we passively "bear witness" to the physical workings of our brain/body)
Some have speculated that it is an emergent property of our biology, directly related to memory. But the verdict is still out. In this regard, I have no definitive opinion on what happens to our consciousness in the infinite number of years that will transpire after we are dead. What I do know is that there are things that exist in the universe about which we are entirely unaware. Our ability to perceive the world was once limited to our biological senses, and has steadily grown through technology. We can now perceive a broader range of the color spectrum. We can capture and translate waves into information. I don't see why there couldn't be something else, that is directly related to our consciousness, that we have not yet been able to perceive other than through our own personal experience of it manifest in that consciousness.
Part of what governs my ethical philosophy is the possibility that our consciousness might occupy different physical bodies at different times. What I mean is, this physical body will retain all of its personality, memories, etc., but the extracorporeal "consciousness" that is perceiving that body's experience might shift from one to another. Or, it might be reborn into a new body at some point. Given that possibility, it seems quite reasonable to strive for a world that minimizing suffering and maximizes the number of living beings that are free to live happy, healthy lives.
Here's an interesting video from a 97-year-old philosopher who talks about what it's like to be old and face death.