... C2(T).(3:22) The proof is complete.Proof of Theorem 3.1 By Lemmas 3.2-3.3, Theorem 2.1 and Sobolev’s embeddingtheorem, we complete the proof of Theorem 3.1.4 Global existence of solutions in ... (4.32 )-(4.33) fromTheorem 2.1, Theorem 3.1, Lemmas 4.2-4.3, (4.41), (4,43) and (4.53). The proof iscomplete.ProofofTheorem4.1Using (1.8),Theorem 2.1, 3.1 and Lemmas 4.2-4.4 and the proper interpolation ... inequality, (2.1) and (2.14), gives (2.19).Proof of Theorem 2.1 By Lemmas 2.1-2.3, we complete the proof of Theorem 2.1.3 Global existence of solutions in H2For external force f(r, t), we...