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Abstract Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKEs) for water waves models. This problem has received intense attention in recent years in the context of semilinear models, such as Schrödinger equations or multidimensional KdV‐type equations. However, our situation here is different since the water waves equations are quasilinear and solutions cannot be constructed by iteration of the Duhamel formula due to unavoidable derivative loss. This is the first of two papers in which we design a new strategy to address this issue. We investigate solutions of the gravity water waves system in two dimensions. In the irrotational case, this system can be reduced to an evolution equation on the one‐dimensional interface, which is a large torus of size . Our first main result is a deterministic energy inequality, which provides control of (possibly large) Sobolev norms of solutions for long times, under the condition that a certain ‐type norm is small. This energy inequality is of “quintic” type: if the norm is , then the increment of the high‐order energies is controlled for times of the order , consistent with the approximate quartic integrability of the system. In the second paper in this sequence, we will show how to use this energy estimate and a propagation of randomness argument to prove a probabilistic regularity result up to times of the order , in a suitable scaling regime relating and . For our second main result, we combine the quintic energy inequality with a bootstrap argument using a suitable ‐norm of Strichartz‐type to prove that deterministic solutions with Sobolev data of size are regular for times of the order . In particular, on the real line, solutions exist for times of order . This improves substantially on all the earlier extended lifespan results for 2D gravity water waves with small Sobolev data. 

Antarctic ice shelves buttress the grounded ice sheet, mitigating global sea level rise. However, fundamental mechanical properties, such as the ice flow law and viscosity structure, remain under debate. In this work, by leveraging remote-sensing data and physics-informed deep learning, we provide evidence over several ice shelves that the flow law follows a grain size–sensitive composite rheology in the compression zone. In the extension zone, we found that ice exhibits anisotropic properties. We constructed ice shelf–wide anisotropic viscosity maps that capture the suture zones, which inhibit rift propagation. The inferred stress exponent near the grounding zone dictates the grounding-line ice flux and grounding line stability, whereas the inferred viscosity maps inform the prediction of rifts. Both are essential for predicting the future mass loss of the Antarctic Ice Sheet.