You might need a log collector like fluentd.

k8s itself won't persist log for you.

If you are using GKE, stackdriver might be an approach (heard, never tried).

The purest and simplest way to get the application log from your pod is using kubectl cp

kubectl cp <pod-name>:/var/etc/logs logs

This will copy the pod logs to your local machine.

However..

That's probably not a good long term solution. I'd recommend:

• Outputting the logs to stdout inside the container, which would mean kubectl logs would become availabla ro you
• Using a fluentd as a sidecar container to manage the logs

More information can be found here

Besides the Fluentd sidecar option described in the other answers, you can also add simple tail -n+1 -f /var/etc/logs sidecar to output your logs to stdout:

apiVersion: v1
kind: Pod
metadata:
  name: mypod
spec:
  containers:
  - name: container
    image: yourimage
    volumeMounts:
    - name: varlog
      mountPath: /var/log
  - name: logs
    image: busybox
    args: [/bin/sh, -c, 'tail -n+1 -f /var/etc/logs']
    volumeMounts:
    - name: varlog
      mountPath: /var/log
  volumes:
  - name: varlog
    emptyDir: {}