High frequencies at which ultrasonic waves travel give rise to nonlinear phenomena. In thermoviscous fluids, these are captured by Blackstock’s acoustic wave equation with strong damping. We revisit in this work its well-posedness analysis. By exploiting the parabolic-like character of this equation due to strong dissipation, we construct a time-weighted energy framework for investigating its local solvability. In this manner, we obtain the small-data well-posedness on bounded domains under less restrictive regularity assumptions on the initial conditions compared to the known results. Furthermore, we prove that such initial boundary-value problems for the Blackstock equation are globally solvable and that their solution decays exponentially fast to the steady state.

超声波传播的高频会引起非线性现象。在热粘性流体中，这些由具有强阻尼的 Blackstock 声波方程捕获。我们在这项工作中重新审视其适定性分析。通过利用该方程由于强耗散而具有的抛物线特征，我们构建了一个时间加权能量框架来研究其局部可解性。通过这种方式，与已知结果相比，我们在初始条件的限制性较少的规则性假设下获得了有界域上的小数据适定性。此外，我们证明 Blackstock 方程的此类初始边值问题是全局可解的，并且它们的解以指数方式快速衰减到稳态。