How to specify "not null" to Spring Data REST / QueryDsl for a HTTP query parameter?

Question

I have Spring Data REST application that uses QueryDsl. My application has a Car entity with a purchaseDate field:

@Entity
@Data
public class Car {

    @Id
    @GeneratedValue(strategy=GenerationType.IDENTITY)
    private Long id;
    
    private LocalDate purchaseDate;
}

The CarRespository is exposed via Spring Data REST at localhost/api/cars:

public interface CarRepository extends CrudRepository<Car, Long>, 
    QuerydslPredicateExecutor<Car>, QuerydslBinderCustomizer<QCar> {
}

An HTTP client can find cars purchased on a date by making a GET request to:

localhost/api/cars?purchaseDate=2023-01-01

Is it possible for a HTTP client to request all cars that have a purchase date (i.e., purchaseDate is not null)? I know that I can add a repository method such as findByPurchaseDateNotNull to accomplish this but was wondering if either

1. the HTTP client can some way specify "not null" or
2. QueryDsl binding could be configured to handle a not null indication from the client