In this paper, we prove local existence and uniqueness of smooth solutions of the Boussinesq equations. We also obtain a blow-up criterion for these smooth solutions. This shows that the maximum norm of the gradient of the passive scalar controls the breakdown of smooth solutions of the Boussinesq equations. As an application of this criterion, we prove global existence of smooth solutions in the case of zero external force.

It has been reported that soybean peptide fractions isolated from Korean fermented soybean paste exert angiotensin I converting enzyme (ACE) inhibitory activity in vitro. In this study, further purification and identification of the most active fraction inhibiting ACE activity were performed, and its antihypertensive activity in vivo was confirmed. Subsequently, a novel ACE inhibitory peptide was isolated by preparative HPLC. The amino acid sequence of the isolated peptide was identified as His-His-Leu (HHL) by Edman degradation. The IC(50) value of the HHL for ACE activity was 2.2 microg/mL in vitro. Moreover, the synthetic tripeptide HHL (spHHL) resulted in a significant decrease of ACE activity in the aorta and led to lowered systolic blood pressure (SBP) in spontaneously hypertensive (SH) rats compared to control. Triple injections of spHHL, 5 mg/kg of body weight/injection resulted in a significant decrease of SBP by 61 mmHg (p < 0.01) after the third injection. These results demonstrated that the ACE inhibitory peptide HHL derived from Korean fermented soybean paste exerted antihypertensive activity in vivo.

Abstract. In this paper we prove the local existence and uniqueness of C 1+γ solutions of the Boussinesq equations with initial data v0, θ0 ∈ C 1+γ , ω0, ∇θ0 ∈ L q for 0 < γ < 1 and 1 < q < 2. We also obtain a blow-up criterion for this local solutions. More precisely we show that the gradient of the passive scalar θ controls the breakdown of C 1+γ solutions of the Boussinesq equations. §1. IntroductionThe interactive motion of a passive scalar (e.g. temperature) and atmosphere with an external potential force is modeled by the following Boussinesq equations:In (1) p denotes the scalar pressure of the fluid flow. It is suggested that these equations have strong resemblance with the 3-D Euler equations in many aspects (see e.g. [7]). In particular the problem of finite time blow-up of smooth solutions of the Boussinesq equations is outstanding as in the case of 3-D Euler equations.In [4], authors proved local existence of solutions of the Boussinesq equations in the Sobolev spaces H m (R 2 ), m > 2, and obtained a blow-up criterion of the smooth solutions. The proofs are similar to Kato's [6] and Beale-Kato-Majda's [2] respectively for the 3-D Euler equations.In this paper we extend the previous results to the case of Hölder continuous initial data. We first prove the unique local existence of the solutions of

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