Strichartz estimates and local existence for the gravity–capillary waves with non-Lipschitz initial velocity

Duvaut and Lions [2] studied the field of velocities and of temperatures in a moving incompressible Bingham fluid endowed with viscosity μ(θ) depending on the temperature θ and established the existence of a weak solution in the case of a two dimensional fluid. However, the problem of uniqueness remained unsolved. The purpose of the present paper is to give an affirmative answer to the problem, that is, to show the local existence (resp. the global existence) in the time and the uniqueness of (strong) solutions in three dimensions under the conditions that (i) the time (resp. the initial velocity and the external force) and (ii) the rate of variation of the viscosity and the yield limit with respect to the temperature are both sufficiently small. It will be easily seen that the global existence and the uniqueness also hold in the two dimensional case whenever the rate (ii) is sufficiently small.

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Effects of capillary waves on the thickness of wetting layers

Journal de Physique ◽

10.1051/jphys:01988004904067500 ◽

1988 ◽

Vol 49 (4) ◽

pp. 675-680 ◽

Cited By ~ 4

Author(s):

S. Chatterjee ◽

E.S.R. Gopal

Keyword(s):

Capillary Waves ◽

Wetting Layers

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A Paradifferential Reduction for the Gravity-capillary Waves System at Low Regularity and Applications

Bulletin de la Société mathématique de France ◽

10.24033/bsmf.2750 ◽

2017 ◽

Vol 145 (4) ◽

pp. 643-710 ◽

Cited By ~ 4

Author(s):

Thibault de Poyferré ◽

Quang-Huy Nguyen

Keyword(s):

Capillary Waves ◽

Low Regularity

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APPLICATION OF THE METHOD SPRINGY DEFORMATIONS OF BARREL DURING SHOT FOR DETERMINING THE INITIAL VELOCITY OF THE SHELL (MINE)

Collection of scientific works of Odesa Military Academy ◽

10.37129/2313-7509.2019.12.1.75-80 ◽

2019 ◽

Vol 1 (12) ◽

pp. 75-80

Author(s):

Ye. Didenko ◽

O. Stepanenko

Keyword(s):

Strain Gauge ◽

Initial Velocity ◽

Radial Direction ◽

Fire Control ◽

Automatic Control Systems ◽

Measurement Results ◽

Initial Resistance ◽

The Moment ◽

The Many ◽

Effective Use

One of the indicators of the effective use of artillery is the accuracy of the fire impact on the objects of enemy. The accuracy of the artillery is achieved by completing the implementation of all measures for the preparation of shooting and fire control. Main measures of ballistic preparation are to determine and take into account the summary deviation of the initial velocity. The existing procedure for determining the summary deviation of the initial velocity for the check (main) cannon of battery leads to accumulation of ballistic preparation errors. The supply of artillery units with means of determining the initial speed of the projectile is insufficient. Among the many known methods for measuring the initial velocity, not enough attention was paid to the methods of analyzing the processes that occur during a shot in the "charge-shell-barrel" system. Under the action of the pressure of the powder gases in the barrel channel and the forces of the interaction of the projectile with the barrel there are springy deformations in the radial direction. To measure springy deformations it is advisable to use strain gauge sensors. Monitoring of deformation in a radial direction by time can be used to determine the moment of passing a projectile past the strain gauge mounted on the outer surface of the barrel. In the case of springy deformations, the initial resistance of the sensor varies in proportion to its value. The speed of the shell (mine) in the barrel can be determined by time between pulses of signals obtained from strain gauges located at a known distance from each other. The simplicity of the proposed method for measuring the initial velocity of an artillery shell provides an opportunity for equipping each cannon (mortar) with autonomous means for measuring the initial velocity. With the simultaneous puting into action of automatic control systems can be automatically taking into account the measurement results. This will change the existing procedure for determining the total deviation of the initial velocity and improve the accuracy, timeliness and suddenness of the opening of artillery fire, which are components of its efficiency.

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A Local Existence and Uniqueness Theorem for a K-BKZ-Fluid.

10.21236/ada130503 ◽

1983 ◽

Cited By ~ 2

Author(s):

Michael Renardy

Keyword(s):

Uniqueness Theorem ◽

Existence And Uniqueness ◽

Local Existence ◽

Existence And Uniqueness Theorem ◽

Local Existence And Uniqueness

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Universal Stokes’s nanomechanical viscometer

Scientific Reports ◽

10.1038/s41598-021-93729-0 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Komal Chaudhary ◽

Pooja Munjal ◽

Kamal P. Singh

Keyword(s):

Electric Field ◽

Real Time ◽

Sample Volume ◽

Capillary Waves ◽

Small Sample ◽

Medical Applications ◽

Rapid Measurement ◽

Single Lens ◽

Universal Applicability ◽

Small Sample Volume

AbstractAlthough, many conventional approaches have been used to measure viscosity of fluids, most methods do not allow non-contact, rapid measurements on small sample volume and have universal applicability to all fluids. Here, we demonstrate a simple yet universal viscometer, as proposed by Stokes more than a century ago, exploiting damping of capillary waves generated electrically and probed optically with sub-nanoscale precision. Using a low electric field local actuation of fluids we generate quasi-monochromatic propagating capillary waves and employ a pair of single-lens based compact interferometers to measure attenuation of capillary waves in real-time. Our setup allows rapid measurement of viscosity of a wide variety of polar, non-polar, transparent, opaque, thin or thick fluids having viscosity values varying over four orders of magnitude from $$10^{0}{-}10^{4}~\text{mPa} \, \text{s}$$ 10 0 - 10 4 mPa s . Furthermore, we discuss two additional damping mechanisms for nanomechanical capillary waves caused by bottom friction and top nano-layer appearing in micro-litre droplets. Such self-stabilized droplets when coupled with precision interferometers form interesting microscopic platform for picomechanical optofluidics for fundamental, industrial and medical applications.

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Full-Waveform Inversion for Imaging Faulted Structures: A Case Study from the Japan Trench Forearc Slope

Pure and Applied Geophysics ◽

10.1007/s00024-021-02727-w ◽

2021 ◽

Author(s):

Ehsan Jamali Hondori ◽

Chen Guo ◽

Hitoshi Mikada ◽

Jin-Oh Park

Keyword(s):

Seismic Data ◽

Initial Velocity ◽

Waveform Inversion ◽

Velocity Model ◽

Control Measures ◽

Japan Trench ◽

Full Waveform Inversion ◽

Full Waveform ◽

Time Migration ◽

Shallow Sediments

AbstractFull-waveform inversion (FWI) of limited-offset marine seismic data is a challenging task due to the lack of refracted energy and diving waves from the shallow sediments, which are fundamentally required to update the long-wavelength background velocity model in a tomographic fashion. When these events are absent, a reliable initial velocity model is necessary to ensure that the observed and simulated waveforms kinematically fit within an error of less than half a wavelength to protect the FWI iterative local optimization scheme from cycle skipping. We use a migration-based velocity analysis (MVA) method, including a combination of the layer-stripping approach and iterations of Kirchhoff prestack depth migration (KPSDM), to build an accurate initial velocity model for the FWI application on 2D seismic data with a maximum offset of 5.8 km. The data are acquired in the Japan Trench subduction zone, and we focus on the area where the shallow sediments overlying a highly reflective basement on top of the Cretaceous erosional unconformity are severely faulted and deformed. Despite the limited offsets available in the seismic data, our carefully designed workflow for data preconditioning, initial model building, and waveform inversion provides a velocity model that could improve the depth images down to almost 3.5 km. We present several quality control measures to assess the reliability of the resulting FWI model, including ray path illuminations, sensitivity kernels, reverse time migration (RTM) images, and KPSDM common image gathers. A direct comparison between the FWI and MVA velocity profiles reveals a sharp boundary at the Cretaceous basement interface, a feature that could not be observed in the MVA velocity model. The normal faults caused by the basal erosion of the upper plate in the study area reach the seafloor with evident subsidence of the shallow strata, implying that the faults are active.

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