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We study the low regularity well-posedness for Cauchy problem of 3Drelativistic Euler equations. Firstly, we introduce a new decomposition forrelativistic velocity and derive new transport equations for vorticity, whichboth play a crucial role in energy and Strichartz estimates. According toSmith-Tataru's approach, we then establish a Strichartz estimate of linear waveequations endowed with the acoustic metric. This leads us to prove a completelocal well-posedness result if the initial logarithmic enthalpy, velocity, andmodified vorticity $(h_0, \bu_0, \bw_0) \in H^s \times H^s \times H^{s_0}(2<s_0<s)$. Therefore, we give an affirmative answer to "Open Problem D"proposed by Disconzi.  Moreover, for $(h_0,{\bu}_0,\bw_0) \in H^{2+} \times H^{2+} \times H^2$, byfrequency truncation, there is a stronger Strichartz estimate for solutions ona short-time-interval. By semi-classical analysis and induction method, thesesolutions can be extended from short time intervals to a regular time interval,and a uniform Strichartz estimate with loss of derivatives can be obtained.This allows us to prove the local well-posedness of 3D relativistic equationsif $(h_0,{\bu}_0,\bw_0) \in H^{2+} \times H^{2+} \times H^2$.

Strichartz estimates and low regularity solutions of 3D relativistic Euler equations