Limit logs in kubernetes
I'm assuming the container engine is docker in which case, you can configure docker to limit the logs written by your pod(s) container(s).
https://docs.docker.com/config/containers/logging/configure/
This is a Community Wiki answer so feel free to edit it and add any additional details you consider important.
As William has already answered this question, I'm only going to add a few details to make this more complete.
Please take a look at Logging Architecture in the official kubernetes docs. As you can read here "Kubernetes currently is not responsible for rotating logs, but rather a deployment tool should set up a solution to address that."
If your container runtime happens to be docker, you can set up your log rotation policy by editing/creating:
/etc/docker/daemon.json(on Linux host)
or:
C:\ProgramData\docker\config\daemon.json(on Windows host)
which may look as follows:
{ "log-driver": "json-file", "log-opts": { "max-size": "10m", "max-file": "3", "labels": "production_status", "env": "os,customer" }}