"assert jurisdiction" is a correct and usable phrase in written English.
Generally, it is used to indicate that a particular authority or group is asserting authority over a certain domain. For example, "The court decided to assert jurisdiction over the dispute."
See, e. g., Academia San Jorge, 234 N.L.R.B. 1181 19788) (advisory opinion stating that Board would not assert jurisdiction over Catholic educational institution which did not meet jurisdictional standards); Windsor School, Inc., 199 N.L.R.B. 457, 200 N.L.R.B. 991 (1972) (declining jurisdiction where private, proprietary school did not meet jurisdictional amounts).
The general counsel, Robert E. Fabricant, issued a memorandum that said "E.P.A. cannot assert jurisdiction to regulate in this area".
McCallion said Kiobel and later rulings "leave the door open" for US courts to assert jurisdiction in genocide cases.
Therefore, we will not decline to assert jurisdiction over these schools on such a basis". 223 N.L.R.B., at 1218.
Iraqi officials have said they would like to prosecute the Blackwater case, but it is extremely unlikely that American authorities would allow them to assert jurisdiction.
This is in large measure due to the requirement that the Court may only assert jurisdiction over states with their consent, which is often withheld.
AOL claims that if the Virginia court found inconsistency, the California court could then re-assert jurisdiction, deny enforcement of the forum selection clause, and allow Mendoza to proceed in the California forum.
Ms. Spaulding said some countries had asserted jurisdiction over war crimes committed anywhere in the world.
The Secretary asserted jurisdiction in this Court by direct appeal under 28 U.S.C. 1252, 1253.
With its new bankruptcy law, China has asserted jurisdiction over who, in the last analysis, controls company assets.
In 1996, the Food and Drug Administration, after having expressly disavowed any such authority since its inception, asserted jurisdiction to regulate tobacco products.
