The Landau equation does not blow up

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Guillen, Nestor, Silvestre, Luis
Format:	Preprint
Published:	2023
Subjects:	Analysis of PDEs 35Q70
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

The Landau equation and Fisher information
by: Guillen, Nestor, et al.
Published: (2025)

The Landau equation as a Gradient Flow
by: Carrillo, José A., et al.
Published: (2020)

Hydrodynamic limit for compressible Navier-Stokes-Vlasov-Poisson equations with local alignment force
by: Su, Yunfei, et al.
Published: (2025)

The Maxwell-Klein-Gordon equation with scattering data
by: Dai, Wei, et al.
Published: (2023)

Mean Field Limit for Congestion Dynamics in One Dimension
by: Kim, Inwon, et al.
Published: (2024)

Global well-posedness and scattering for nonlinear Schrödinger equations with combined nonlinearities in the radial case
by: Cheng, Xing, et al.
Published: (2014)

Quantitative asymptotic stability of the quasi-linearly stratified densities in the IPM equation on the three fundamental domains
by: Jo, Min Jun, et al.
Published: (2022)

On the existence of solutions to the multi-species Landau equation
by: Junné, Jonathan, et al.
Published: (2025)

A derivation of the time dependent von Kármán equations from atomistic models
by: Buchberger, David, et al.
Published: (2024)

Cnoidal Waves for the cubic nonlinear Klein-Gordon and Schrödinger Equations
by: de Loreno, Guilherme, et al.
Published: (2021)

High-order time splitting methods for the nonlinear Gross-Pitaevskii equation
by: Ben, Roberto, et al.
Published: (2026)

Hydrodynamic limit of a kinetic flocking model with nonlinear velocity alignment
by: Black, McKenzie, et al.
Published: (2023)

Uniform Decaying Property of Solutions for Anisotropic Viscoelastic Systems
by: de Hoop, Maarten V., et al.
Published: (2023)

Radiative Vlasov-Maxwell Equations
by: Constantin, Peter, et al.
Published: (2025)

First order non-instantaneous corrections in collisional kinetic alignment models
by: Kanzler, Laura, et al.
Published: (2025)

Scattering map for the Vlasov--Poisson system with a repulsive harmonic potential
by: Huang, Wenrui, et al.
Published: (2026)

Asymptotic Stability for Relativistic Vlasov-Maxwell-Landau System in Bounded Domain
by: Dong, Hongjie, et al.
Published: (2023)

Scattering and blow up for nonlinear Schrödinger equation with the averaged nonlinearity
by: Kawakami, Jumpei
Published: (2023)

The blow-up dynamics for the divergence Schrödinger equations with inhomogeneous nonlinearity
by: Zheng, Bowen, et al.
Published: (2024)

The Local-well-posedness of the relativistic Vlasov-Maxwell-Landau system with the specular reflection boundary condition
by: Dong, Hongjie, et al.
Published: (2023)

Existence of solutions of semilinear wave equations with time-dependent propagation speed and time derivative nonlinearity
by: Tsutaya, Kimitoshi, et al.
Published: (2025)

Schrödinger system with quintic nonlinearity: spectral stability of multiple sign-changing periodic waves
by: de Loreno, Guilherme, et al.
Published: (2026)

A spectral method for dispersive solutions of the nonlocal Sine-Gordon equation
by: Coclite, A., et al.
Published: (2024)

Dispersive blow-up for solutions to three dimensional generalized Zakharov-Kuznetsov equations
by: Ban, Yingzhe, et al.
Published: (2024)

Linearized dynamic stability for vortices of Ginzburg-Landau evolutions
by: Palacios, José M., et al.
Published: (2024)

Existence and weak-strong uniqueness of measure solutions to Euler-alignment/Aw--Rascle--Zhang model of collective behaviour
by: Woźnicki, Jakub, et al.
Published: (2025)

Sparse identification of nonlocal interaction kernels in nonlinear gradient flow equations via partial inversion
by: Carrillo, Jose A., et al.
Published: (2024)

Global existence and blow-up for the variable coefficient Schrödinger equations with a linear potential
by: Zheng, Bowen, et al.
Published: (2024)

Energy decay and blow-up of viscoelastic wave equations with polynomial nonlinearity and damping
by: Peng, Qingqing, et al.
Published: (2025)

Well-posedness of diffusion-aggregation equations with bounded kernels and their mean-field approximations
by: Chen, Li, et al.
Published: (2023)

Fluctuations around the mean-field limit for attractive Riesz potentials in the moderate regime
by: Chen, Li, et al.
Published: (2024)

The rigorous derivation of Vlasov equations with local alignments from moderately interacting particle systems
by: Wang, Jinhuan, et al.
Published: (2024)

The entropy production is not always monotone in the space-homogeneous Boltzmann equation
by: Silvestre, Luis
Published: (2026)

The propagation of regularity and dispersive blow-up phenomenon to higher-order generalized KdV equations
by: Shan, Minjie
Published: (2024)

Dynamics for the corotational energy-critical wave map equation with quantized blow-up rates
by: Li, Ze, et al.
Published: (2023)

Convergence of a finite-volume scheme for aggregation-diffusion equations with saturation
by: Gómez-Castro, David
Published: (2025)

Global well-posedness and scattering for the massive Dirac-Klein-Gordon system in two dimensions
by: Bejenaru, Ioan, et al.
Published: (2025)

The Lake equation as a supercritical mean-field limit
by: Rosenzweig, Matthew, et al.
Published: (2024)

Regularity and Uniqueness for a Model of Active Particles with Angle-Averaged Diffusions
by: Alasio, Luca, et al.
Published: (2025)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
language	"en"
VUFIND_SESSION	"13d103e73c3f9db994d2fb0343e30fe7"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790836405.0729 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "13d103e73c3f9db994d2fb0343e30fe7" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; language=en; VUFIND_SESSION=13d103e73c3f9db994d2fb0343e30fe7"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"8065"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2311_09420/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2311_09420/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790836405.0688
REQUEST_TIME	1790836405

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
language	"en"
VUFIND_SESSION	"13d103e73c3f9db994d2fb0343e30fe7"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790836405.0729 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "13d103e73c3f9db994d2fb0343e30fe7" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; language=en; VUFIND_SESSION=13d103e73c3f9db994d2fb0343e30fe7"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"8065"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2311_09420/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2311_09420/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790836405.0688
REQUEST_TIME	1790836405

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: