page_title: Picard–Lindelöf theorem
hierarchical_section_title: Picard–Lindelöf theorem
context_page_description: In mathematics – specifically, in differential equations – the Picard–Lindelöf theorem, Picard's existence theorem, Cauchy–Lipschitz theorem, or existence and uniqueness theorem gives a set of conditions under which an initial value problem has a unique solution.
  The theorem is named after Émile Picard, Ernst Lindelöf, Rudolf Lipschitz and Augustin-Louis Cauchy.
  Consider the initial value problem
  Suppose f is uniformly Lipschitz continuous in y and continuous in t, then for some value ε > 0, there exists a unique solution y to the initial value problem on the interval.
context_section_description: In mathematics – specifically, in differential equations – the Picard–Lindelöf theorem, Picard's existence theorem, Cauchy–Lipschitz theorem, or existence and uniqueness theorem gives a set of conditions under which an initial value problem has a unique solution.
  The theorem is named after Émile Picard, Ernst Lindelöf, Rudolf Lipschitz and Augustin-Louis Cauchy.
  Consider the initial value problem
  Suppose  f  is uniformly Lipschitz continuous in y (meaning the Lipschitz constant can be taken independent of t) and continuous in t, then for some value ε > 0, there exists a unique solution y(t) to the initial value problem on the interval .
caption: Navier–Stokes differential equations used to simulate airflow around an obstruction.