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Gradient Blow-Up for Dispersive and Dissipative Perturbations of the Burgers Equation
We consider a class of dispersive and dissipative perturbations of the inviscid Burgers equation, which includes the fractional KdV equation of order
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Curvature Blow-up and Mass Inflation in Spherically Symmetric Collapse to a Schwarzschild Black Hole
We study the black hole interiors of spacetimes arising from gravitational collapse within the spherically symmetric Einstein-scalar field system. By...
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Construction of Blow-Up Manifolds to the Equivariant Self-dual Chern–Simons–Schrödinger Equation
We consider the self-dual Chern–Simons–Schrödinger equation (CSS) under equivariance symmetry. Among others, (CSS) has a static solution Q and the...
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Classification of the Blow-Up Behavior for a Semilinear Wave Equation with Nonconstant Degenerate Coefficients
We consider a nonlinear wave equation with nonconstant coefficients. In particular, the coefficient in front of the second-order space derivative is...
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Sharp Universal Rate for Stable Blow-Up of Corotational Wave Maps
We consider the energy-critical (corotational) 1-equivariant wave maps into the two-sphere. By the seminal work (Raphaël and Rodnianski in Publ Math...
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Perturbation at Blow-Up Time of Self-Similar Solutions for the Modified Korteweg–de Vries Equation
We prove a first stability result of self-similar blow-up for the modified Korteweg–de Vries equation on the line. More precisely, given a...
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Global Existence and Finite-Time Blow-Up for a Nonlinear Nonlocal Evolution Equation
We study the Cauchy problem for a nonlinear nonlocal evolution equation arising in the study of oceanic flows in equatorial regions. We present a...
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On Blow-up and Global Existence of Weak Solutions to Cauchy Problem for Some Nonlinear Equation of the Pseudoparabolic Type
AbstractWe briefly present the results of the investigation of the Cauchy problem for a nonlinear pseudoparabolic equation that is a mathematical...
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Blow-up of waves on singular spacetimes with generic spatial metrics
We study the asymptotic behaviour of solutions to the linear wave equation on cosmological spacetimes with Big Bang singularities and show that...
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Local-in-Space Blow-up for a Weakly Dissipative Generalized Two-Component Camassa–Holm System
We investigate the blow-up issue of a weakly dissipative generalized two-component Camassa–Holm system. We establish a local-in-space blow-up result...
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Global Existence and Blow-Up Phenomena for the Hunter-Saxton Equation on the Line
In this paper, we consider the Cauchy problem for the Hunter-Saxton (HS) equation on the line. Firstly, we establish the local well-posedness for the...
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Blow-up Analysis for the \({\varvec{ab}}\)-Family of Equations
This paper investigates the Cauchy problem for the ab -family of equations with cubic nonlinearities, which contains the integrable modified...
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Blow up Criteria for the 2D Compressible Navier-Stokes Equations in Bounded Domains with Vacuum
In this paper, we study the compressible barotropic Navier-Stokes equations in a general two-dimensional bounded domain with the Navier-slip boundary...
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Soliton, blow up, and shock-like ion-acoustic waves in magnetized plasma at Venus’ ionosphere
The propagation properties of various nonlinear electrostatic structures, namely, soliton, shocklike, periodic, and explosive waves, are explored in...
