Note 13 - Related Party Transactions (Details Textual) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
	Mar. 29, 2023	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2024	Sep. 30, 2023	Dec. 31, 2023	Nov. 06, 2022
Accounts Payable, Current		$ 4,866		$ 4,866		$ 4,632
Related Party [Member]
Accounts Payable, Current		100		100		100
Glytech License Agreement [Member]
Related Party Transaction, Amounts of Transaction		0	$ 100	300	$ 200
Glytech License Agreement [Member] | NRX Pharmaceuticals, Inc [Member] | Minimum [Member]
Investment Owned, Fair Value							$ 50,000
Consultation Agreement with Dr. Jonathan Javitt [Member]
Related Party Transaction, Amounts of Transaction		200	200	200	700
Consultation Agreement with Zachary Javitt [Member]
Related Party Transaction, Amounts of Transaction		200	$ 100	200	$ 100
Consulting Agreement, Annual Payment	$ 600
Consulting Agreement, Monthly Payment	100
Consulting Agreement, Performance Bonus, Target Value	$ 300
Accrued Bonuses, Current		$ 300		$ 300		$ 200
Consultation Agreement with Zachary Javitt [Member] | Restricted Stock [Member]
Share-Based Compensation Arrangement by Share-Based Payment Award, Non-Option Equity Instruments, Granted (in shares)	50,000
Consultation Agreement with Zachary Javitt [Member] | Restricted Stock [Member] | Unrestricted Upon New Drug Application Date [Member]
Share-Based Compensation Arrangement by Share-Based Payment Award, Non-Option Equity Instruments, Granted (in shares)	25,000
Consultation Agreement with Zachary Javitt [Member] | Restricted Stock [Member] | Unrestricted Upon New Drug Approval Date [member]
Share-Based Compensation Arrangement by Share-Based Payment Award, Non-Option Equity Instruments, Granted (in shares)	25,000