use instance property as v-model - vue.js

Question

I use a Form object to handle all my input fields and validation/errors etc.
new Vue({
el: '#root',
data: {
form: { trainer: '' }
}
And I can use it as v-model like this:
<input v-model='form.trainer' name='trainer'>
I would like to make the form an instance property, because I have to pass it to all my components at the moment.
Vue.prototype.$form = {trainer: ''}
new Vue({ el: '#root' });
However, its not reactive anymore:
<input v-model="$form.trainer">
<span v-text="$form.trainer"></span>
Changes to the input are not reflected on the span.
Is there a solution to use a instance property as v-model?

Answer 1

Using Global Mixin:
You can use Global Mixin and then add form: { trainer: '' } to it and then this option will be available in every Vue instance created afterwards like:
// inject a handler for `myOption` custom option
Vue.mixin({
data: function () {
return {
form: { trainer: '' }
}
}
})
and then you can use it like normal component data option:
<input v-model="form.trainer">
<span v-text="form.trainer"></span>
Demo:
// inject a handler for `myOption` custom option
Vue.mixin({
data: function() {
return {
form: { trainer: '' }
}
}
})
// Define a new component called trainer
Vue.component('trainer', {
template: `<div>
<input v-model="form.trainer">
<span v-text="form.trainer"></span>
</div>
`
})
new Vue({
el: "#myApp",
})
<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.5.17/vue.min.js"></script>
<link href="https://stackpath.bootstrapcdn.com/bootstrap/4.4.1/css/bootstrap.min.css" rel="stylesheet">
<div id="myApp">
<trainer></trainer>
<trainer></trainer>
</div>
Demo #2:
var trainer2Data = {
form: { trainer: '' }
}
Vue.mixin({
data: function() {
return trainer2Data;
}
})
// Define a new component called trainer2
Vue.component('trainer2', {
template: `<div>
<input v-model="form.trainer">
<span v-text="form.trainer"></span>
</div>
`
})
new Vue({
el: "#myApp",
})
<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.5.17/vue.min.js"></script>
<link href="https://stackpath.bootstrapcdn.com/bootstrap/4.4.1/css/bootstrap.min.css" rel="stylesheet">
<div id="myApp">
<trainer2></trainer2>
<trainer2></trainer2>
</div>