A "weak solution" refers to a type of solution for differential equations that may not be smooth or even continuous but still satisfies the equation in a broader sense. Instead of requiring the solution to meet strict criteria, weak solutions allow for more flexibility, making it possible to find solutions in cases where traditional methods fail. This concept is particularly useful in the study of partial differential equations. Weak solutions are often defined using the concept of test functions, which are smooth functions that help to evaluate the behavior of the weak solution. By integrating the weak solution against these test functions, mathematicians can derive meaningful results without needing the solution to be differentiable everywhere. This approach is essential in fields like fluid dynamics and material science, where solutions may exhibit irregularities.