vue.js – I cannot npm install with just created vue2 + vuetify proj

As you are seemingly on an old version of npm (<=6.x) you need to install the peer dependency yourself:

npm i -D @vue/cli-service@5.0.0 

After installing the dependency, edit your package.json and insert this block on the top level, right after the "devDependencies" object:

"peerDependencies": {
    "@vue/cli-service": "^5.0.0"
}

and remove that dependency from the "devDependencies" object.

If you don’t want to deal with peer dependencies yourself, upgrade your node and npm version. To upgrade npm only:

npm i -g npm