An application currently running on the Kubernetes cluster employs the nginx web server. The Nautilus application development team has introduced some recent changes that need deployment. They've crafted an image nginx:1.19 with the latest updates.

Execute a rolling update for this application, integrating the nginx:1.18 image. The deployment is named nginx-deployment.

Ensure all pods are operational post-update.

thor@jumphost ~$ kubectl get deployments
NAME               READY   UP-TO-DATE   AVAILABLE   AGE
nginx-deployment   3/3     3            3           16s
thor@jumphost ~$ kubectl get pods
NAME                               READY   STATUS    RESTARTS   AGE
nginx-deployment-989f57c54-7r2gs   1/1     Running   0          26s
nginx-deployment-989f57c54-c5jmq   1/1     Running   0          26s
nginx-deployment-989f57c54-lhg7b   1/1     Running   0          26s
thor@jumphost ~$ kubectl set image deployment nginx-deployment nginx-container=nginx:1.18
deployment.apps/nginx-deployment image updated
thor@jumphost ~$ kubectl get pods
NAME                                READY   STATUS    RESTARTS   AGE
nginx-deployment-58cf54c7f6-lf6ft   1/1     Running   0          22s
nginx-deployment-58cf54c7f6-r94hk   1/1     Running   0          15s
nginx-deployment-58cf54c7f6-tkd8x   1/1     Running   0          13s
thor@jumphost ~$ kubectl get deployments
NAME               READY   UP-TO-DATE   AVAILABLE   AGE
nginx-deployment   3/3     3            3           103s
thor@jumphost ~$ kubectl rollout status deployment nginx-deployment
deployment "nginx-deployment" successfully rolled out